fcla / changes.txt

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v3.00 2012/xx/xx
~~~~~~~~~~~~~~~~
New:  Diagrams NSLT, SLT (surjective linear transformations)
New:  Diagrams KPI, IVLT (pre-images, invertible linear transformations)
New:  Diagram KRI (kernel and range isomorphisms)
New:  Exercise NM.T31 (with solution)
New:  Exercises LT.T30 and LT.T31
New:  Exercise LISS.T51, converse of Theorem VRRB
New:  Exercise LISS.T20, subset of linearly independent set is linearly independent
New:  Reading Questions, Section OD
New:  Diagram AIVS, Section IVLT
New:  Discussion following Theorem OBNM
New:  Exercises MM.T35, OD.T10, OD.T20
New:  Exercise VR.M20 (Tyler Ueltschi)
Edit:  Explained  min(m,n)  in Exercise PD.T15
Edit:  More on induction in Proof Technique I (Dan Messenger)
Edit:  Added multiplicities to Solution EE.C19 (Duncan Bennett)
Edit:  Subsection IVLT.SLELT, reference Definition MVP for T's definition (Kyle Whitcomb)
Edit:  Completed Solution ILT.C27 (Duncan Bennett)
Edit:  About 130 line-break adjustments, for 5 inch text width at 10pt
Edit:  Edits, Subsection CB.CELT
Edit:  Solution SLT.C29, added solution to surjective question (Dan Messenger)
Change:  Replaced Definition RR by an informal discussion
Change:  Definition TSVS renamed as Definition SSVS
Change:  Proof Technique D: discussion about definitions as nouns, adjectives
Change:  Subsection PD.DS (Direct Sums) removed, now in second volume
Change:  Subsection MM.PMM, before Theorem MMIP, conjugate fixed to reflect theorem (Dave Perkins)
Change:  Solution SLT.C25 no longer uses rank of a linear transformation (Becca Ebert)
Change:  Proof of Theorem OD rewritten
Typo:  Proof of Theorem SLSLC: Doubled text macro in source (Glenna Toomey)
Typo:  Solution S.T30: Corrected bolding on 'Proof' (Glenna Toomey)
Typo:  LaTeX/XML formatting in Solutions RREF.C11, RREF.C13, RREF.C16 (Caden Robinson)
Typo:  LaTeX/XML formatting in Solutions SSLE.M10, LISS.C21, B.C11 (Caden Robinson)
Typo:  Exercise TSS.T20, fixed link to notation (Caden Robinson)
Typo:  Spelling and grammar, Annotated Acronyms VS (Nick Butterfield)
Typo:  LaTeX/XML formatting, Proof of SLSLC, discussion after VSPCV
Typo:  Several LS(A,b) without bold  b  vector (Sophie Bartolomeo)
Typo:  Sign change deep in Example SSP (Dan Messenger)
Typo:  LaTeX/XML formatting in Exercises MISLE.C41, MINM.C40 (Caden Robinson)
Typo:  LaTeX/XML formatting in Exercise VS.M12 (Ameneh McCullough)
Typo:  Removed bad forward reference in Exercise LISS.C21 (Tyler Ueltschi)
Typo:  LaTeX/XML formatting in Exercises LISS.T50, D.M20 (Becca Ebert)
Typo:  Grammar in proof of Theorem TSS (Frankie de Lavis)
Typo:  Spelling in Preface "eigenvvectors"
Typo:  LaTeX/XML formatting in Exercise PD.C40 (Becca Ebert)
Typo:  Stray percent sign in Example D33M (Glenna Toomey)
Typo:  Incorrect initial matrix in Solution DM.C30 (Julie Nelson)
Typo:  Spelling in introduction to Section EE "ethe" (Liz Meuci)
Typo:  Spelling in Section VS "be we" to "but we" (Caden Robinson)
Typo:  Reference in Example VSM is to a definition, not example (Caden Robinson)
Typo:  LaTeX/XML formatting in Reading Question LISS.2 (Caden Robinson)
Typo:  LaTeX/XML formatting in Solutions EE.C23, EE.C24, EE.C25 (Caden Robinson)
Typo:  LaTeX/XML formatting in Example DAB (Ben Boe)
Typo:  Exercise PEE.T22 "had" to "has" (Dan Messenger)
Typo:  Example SAV, misleading misalignment in matrix (Mitch Benning, Davis Schubert)
Typo:  LaTeX/XML formatting in Exercise, Solution RREF.M40 (Aidan Meacham)
Typo:  LaTeX/XML formatting in Solution ILT.C40 (Julie Nelson)
Typo:  Section LT, after Example MFLT, "not an accident" (Kyle Whitcomb)
Typo:  Section SLT, before Diagram SLT, domain/codomain confusion (Kyle Whitcomb)
Typo:  Section IVLT, after Definition IVS, "given", "a" reversed (Kyle Whitcomb)
Typo:  LaTeX rules for fill-in-the-blank exercises (Julie Nelson)
Typo:  LaTeX/XML formatting in Solution IVLT.C20 (Julie Nelson)
Typo:  LaTeX/XML formatting in Solution LT.C43 (Duncan Bennett)
Typo:  Example SEEF, mis-aligned "M = " (Dave Perkins)
Typo:  Example SPIAS, scalar in C^3 (Nick Butterfield)
Typo:  LaTeX/XML formatting, \matrixrep in Theorem OBUTR proof
Typo:  LaTeX/XML formatting, \lt in Theorem VRI proof (Stephen Gower)
Typo:  Implication arrow in wrong direction, Theorem IMR (Dan Messenger)
Typo:  Example LIC, second sentence, in/dependence (Aidan Meacham)
Typo:  Solution B.T50, missing implication arrows
Typo:  Sage CELT, needed symbolic variables (Tyler Ueltschi)

MAJOR SOURCE FORMAT CHANGE
~~~~~~~~~~~~~~~~~~~~~~~~~~

Version 2.99 is the last version that is guaranteed to compile from the
LaTeX sources initiated in December 2003.  Content has all migrated
to an XML format, using a one-off conversion process, custom XML tags
and LaTeX syntax for in-line and displayed mathematics.

Changes to the LaTeX sources subsequent to Version 2.99 are
designed to support the automated conversion to XML and some
new environments (e.g. "introduction", "para", "graphics") are
not implemented in the corresponding style files.  Additional
content has been integrated, such as Tikz graphics and the Sage
vignettes.

v2.99 source (as published, or with additions) may be recreated
in two ways:
(a) rolling back to the version "2.99" Mercurial tag (published version)
(b) in the new "latex" subdirectory (source with additions).


v2.99 2012/10/13
~~~~~~~~~~~~~
Omission:  Corrected discussion of inner product definition (Diego Barreiro)
Typo:  Set S is really T, discussion following Theorem BCS (Diego Barreiro)
Typo:  Miscellaneous small corrections, Sections MM, MISLE, VS, S (Diego Barreiro)
Typo:  Solution SSLE.M70, spelling (Becca Ebert)
Typo:  Small fix to new version of VO.T05 (Nick Butterfield)
Typo:  Solution LI.M50, "we that" becomes "we find that" (Dan Messenger)
Typo:  Several "the the" (Jack Gilbert)
Edit:  Theorem SLSLC statement: clarified that the vector  x  has  n  entries (Jack Gilbert)
Change:  Alignment of several exercises in Section RREF (Ameneh McCullough)
Change:  Solutions EE.C23, EE.C24 reformatted
Change:  Exercises VO.T05, VO.T06, VO.T07: proofs re-written

v2.90  2012/06/17
~~~~~~~~~~~~~
MAJOR CHANGE:
    The inner product is now "reversed" from what it was formerly.
    Specifically, the entries of the *first* vector are conjugated now.
  Rationale:
    This will make properties for numerous matrix decompositions and other
    aspects of orthogonality simpler and more natural.  This is already
    evident as several proofs have been shortened and simplified.
  Changes:
    Definition IP - root cause
    Theorem IPSM - now scalar multiples of first vector
                   "come out" conjugated
    Theorem MMIP - conjugate and transpose both now affect first vector
    Theorem GSP - order in inner products reversed.  Necessary for the proof
                  but also preserves any existing computations
    Theorem COB - order in inner products reversed.  Necessary for the proof
                  but also preserves any existing computations
    Proofs - Many proofs depend on the five items above and have been
             rewritten.  Generally they are equivalent or simpler.  These
             changes are not documented here.  See the revision history, which
             is organized by section, or search on uses of the theorems above.
    Limitations - Changes only go through Section CB.  Remaining sections will
                  be adjusted as edited.
                  
New:  Exercise HSE.T11, equivalent systems, both homogeneous, or both not (Robert Beezer)
New:  Exercise SSLE.M14, 'time flies like...' (Gary Gordon)
Typo:  Extra "a" in Section VO (Aaron Taylor)
Typo:  a/the Example LINSB (Zeke Rosenberg)
Typo:  "see" missing from Solution LDS.C50 (Aaron Taylor)
Typo:  "of" missing from Subsection MISLE.MI (Zeke Rosenberg)
Typo:  Exercise and Solution SS.M12 needs set brackets in spans (Cliff Berger)
Typo:  Proof of Theorem NI has bad reference to Theorem NMRRI (Troy Cornelius)
Typo:  Adjusted subsection acronym to FS.CCS (Troy Cornelius)
Typo:  Solution MO.C13, alpha = 2 (Preston Van Buren)
Typo:  Exercises MO.C12, MO.C13 are matrix equations (Preston Van Buren)
Typo:  Subsection LISS.LI, bad reference to column vector linear independence (Troy Cornelius)
Typo:  Solution MINM.M15, nonsingular should be singular (Preston Van Buren)
Typo:  Exercise MINM.M10, missing comma (Sophie Scheller)
Typo:  Theorem DNLT, missing "if" (Shepherd Engle)
Typo:  Solution LISS.C26, five matrices span, not four (Alden Horowitz)
Typo:  Two minor ones, LISS reading questions (Sophie Scheller, Preston Van Buren)
Typo:  Subsection EE.EEE, bad reference to determinant definition (David Farmer)
Typo:  Example KVMR, linear transformation definition fixed (Ryan Walch)
Typo:  Example CIVLT, kernel should be trivial (Ryan Walch, Cliff Berger)
Typo:  Solution LISS.C22, dro is for (Cliff Berger)
Typo:  Section MINM, The is This (Aaron Taylor)
Typo:  Section MINM, calls is call (Troy Cornelius)
Typo:  Example VRP2, second basis is C (Preston Van Buren)
Typo:  Subsection NLT.CFNLT, dangling reference deleted (Shepherd Engle)
Typo:  Exercise VS.M21, vector multiplication is scalar multiplication (Davis Shurbert)
Typo:  Subsection MR.NRFO, reference to Theorem ME is Theorem EMP (Cliff Berger)
Typo:  Solution S.C17, matrix needs augmenting (Alden Horowitz)
Typo:  Solution SSLE.C51, removed asterisk as multiplication
Typo:  Solution PD.C40, vector space is P_4, not P_5 (Cliff Berger)
Typo:  Exercise ILT.T15, kernels, not null spaces
Typo:  Solution CB.C41, S_{22} is domain (Preston Van Buren)
Typo:  Archetypes, inverse linear transformation check reordered (Preston Van Buren)
Addition: Solution IVLT.T15 cites Definition ROLT (Alex King)
Change: Reworded Exercise TSS.M45 (Davis Shurbert)
Change: Subsection HP.DMHP, converted citation request (Troy Cornelius)
Change: Theorem SSS, clarified span is a subset, fixed missing brackets (Luran Li)
Change: Exercise NM.T10, Solution NM.T10 slightly reworked
Change: Exercises VO, reformatted 3 problem numbers
Change: Exercise VS.M12, Exercise VS.M13, changed addition symbol
Change: Reading Question MISLE.1, totally new matrix, with fraction-free inverse

v2.30  2011/12/23
~~~~~~~~~~~~~
Typo:  Bad subscript in proof of Theorem RREFU (Antti Tuppurainen)
Typo:  Misspellings in Solution LISS.C26 (Robert Tunney)
Typo:  Misspellings in Annotated Acronyms VS (Robert Tunney)

v2.23  2011/11/30
~~~~~~~~~~~~~
Typo:  Solution DM.M16, one root is -4 (Tuo "Thomas" Huang)
Typo:  Solution LI.M21, alpha_3 subscripts fixed (Robert Tunney)
Typo:  Exercise MO.C10, sign change on beta (Jessica Norworth, Robert Tunney)
Typo:  Exercise SLT.C24, removed non-existent coefficient e (Audrey Tiew)
Typo:  Example SSP4, two instances of 24 alpha_2 changed to 24 alpha_4
Typo:  Section LC: "will be appear again" fixed (David Randolph)
New:  Exercise VS.T30, Property O is just for 1 (James Gallagher)
New:  Exercise EE.T15, two definitions of characteristic polynomial
New:  Exercises M60 in LT, ILT, SLT, IVLT, MR about the zero linear transformation
New:  Exercise IVLT.T40, composition invertible, then so are parts
New:  Exercises MR.M80,M81,M82,M83: old matrix results in linear transformation terms
Change:  Reading Question LDS.1
Change:  Exercise SSLE.M70 fixed to work over complexes for one and zero solutions (Don Kreher)
Change:  Improve discussion following Theorem EMMVP (Robert Tunney)
Change:  Improve Solution SSLE.M10 (Robert Tunney)
Change:  Exercise LI.C22, totally replaced to make linear combination simpler computationally (Robert Tunney)
Change:  Improve wording of Definition EEF (Zoltan Toth)
Change:  Careful reductions to echelon form in RREF run on index j (Ben Zeilstra)

v2.22  2010/04/21
~~~~~~~~~~~~~
Typo:  Section LT intro, "He" -> "Here" (Sigrun Bodine)
Typo:  Section LT, "how how" (Jinshil Yi)
Typo:  Section EE, "take the each" (Jinshil Yi)
Typo:  Theorem DEM, third part of proof, confused subscripts (Jinshil Yi)
Typo:  Subsection ILT.ILTLI, "if" -> "in" (Shepherd Engle)
New:  Expanded intro to Section MISLE
New:  Expanded Solution MISLE.T10
New:  Added Theorem NPNT to Annotated Acronyms in Chapter M
New:  Added proper citations in first half of proof of Theorem TSS
New:  Added m <= n to hypotheses of Theorem DSFB (Jinshil Yi)
Change:  Exercise LISS.T40, removed references to a basis, reworded (Jinshil Yi)
Change:  First half of proof of Theorem NI shortened
Removed:  Exercises MM.M30, MM.M31.  Duplicated in MM.T41.

v2.21  2010/03/10
~~~~~~~~~~~~~
Typo:  Solution ILT.T20, null spaces of linear transformations should be kernels (Scott Macha, Lisa Kant)
Typo:  Technique DC, "anitderivative" (Jinshil Yi)
Typo:  "taht", "scalked" (Jinshil Yi)
Typo:  Section VO, last paragraph, Property ACC corrected to AAC (David Eva)
Edit:  Part 1 of Definition RREF slightly reworded.
Edit:  Row operation examples and solutions reformatted
Edit:  Improved \setparts macro
Edit:  Various clean-up in Chapters SLE, V
New:  Exercise HSE.T12 (Ivan Kessler)
New:  Exercise NM.T12

v2.20  2009/08/17
~~~~~~~~~~~~~
Typo:  Theorem GESD, missing power of  m  three times in kernels at very end. (Zoltan Toth)
Typo:  Section JCF, Subsection JCF, introductory paragraph, two words missing. (Zoltan Toth)
Typo:  Example DSM22, Coefficient of d, second equation, changed to -2. (Joe Gain)
Typo:  Theorem DERC, "rows r and s" changed to "rows s and t." (Charles Ganiear)
Typo:  Exercise SLT.C23, x^4 changed to x^3. (Tanya Leise)
Typo:  Solution MR.C40, stray S changed to R. (Tanya Leise)
Typo:  Exercise IVLT.C25, codomain to C^3 in part 5. (Tanya Leise)
Notation:  Linear transformation definitions now use \rightarrow, not \mapsto. (Tanya Leise)
Change: Solutions RREF.C10-C19 rewritten to not reference next section (Manley Perkel)
Add:  Example RREF.RREF has additional illustration of sets D and F. (Manley Perkel)
Add:  Solution RREF.T10 has some extra explanation.  (Robert Beezer)
New:  Definitions SSLE and SSSLE in Section SSLE making "solution" a precise term
New:  Exercises TSS.M46, TSS.M70, TSS.T20 (r, D, F notation) (Manley Perkel)
New:  Exercise LI.M51 (Manley Perkel, Rob Beezer)
New:  Exercises LI.M20, LI.M21 (Rob Beezer)
New:  Edition formatted for Kindle DX

v2.12  2009/04/08
~~~~~~~~~~~~~
Typo:  Proof Technique I, fixed algebra in proof for sum of integers (William Haynes)
Typo:  Example CFV, for Archetype E, leading 1 is now row 3, column 5 (William Haynes)
Typo:  Theorem CFNLT, table at end and following.  Subscripts d corrected to p. (Zoltan Toth)
Typo:  Theorem GESD, 2 typos, and a missing identity matrix at end. (Zoltan Toth)
Typo:  Theorem GESD, T:V->V in hypothesis.
Typo:  Solution EE.C24, wandering minus sign in eigenvector for eigenvalue 3. (Hung An Kim)
Typo:  Removed ten stray instances of exam "points."  (Tanya Leise)
Change:  Theorem HMIP, second half of proof streamlined (Manley Perkel)
Change:  Example VSF generalized slightly (Manley Perkel)
New:  Enhancements to Definition VS and associated commentary (Manley Perkel)
New:  Exercise O.M60 (Manley Perkel)
New:  Exercises MO.T30--MO.T37, sequence of proofs about skew-symmetric matrices (Manley Perkel)


v2.11  2009/02/18
~~~~~~~~~~~~~
New:  Links in problem statements to solutions vanish if solutions are omitted (Nancy Neudauer)
New:  Edition file for Pacific University course  (Nancy Neudauer)
New:  Warning after Definition RREF abut the use of sets D and F for any matrix (Nancy Neudauer)
New:  Exercises LI.C20-25 now ask for relation of linear dependence for linearly dependent sets (Manley Perkel)
New:  Exercises VO.T30,T31,T32 about vector subtraction
New:  Comments at the end of Section VO about subtraction, parentheses (Manley Perkel)
New:  Partial fraction example added to Proof Technique DC as an example (Manley Perkel)
Change:  Solution VS.M21 duplicates VS.M20, replaced with accurate solution (Tanya Leise)
Change:  Definition A (adjoint) shouldn't require the matrix to be square (Manley Perkel)
Change:  Example SCAB no longer mentions V, it was not used (Manley Perkel)
Change:  Complex numbers in Subsection CNO.CCN written as Greek letters (Manley Perkel)
Change:  Various grammar, spelling and other edits (Manley Perkel)
Typo:  Definition F, four V's corrected to be F's (Tomas da Silva Martins de Godoi)
Typo:  Theorem SLSLC, four  1 <= i <= n  replaced with  1 <= i <= m (Valeron JC)
Typo:  Solution RREF.M50 now mentions the number of trucks in the solution (Manley Perkel)


v2.10  2009/01/11
~~~~~~~~~~~~~
Typo:  Archetype R, inverse linear transformation, 221/4 corrected to 221/2 (David Braithwaite)
Typo:  Theorem CFNLT, third paragraph.  Two s_i corrected to s_p (Zoltan Toth)
Typo:  Theorem GESD, "scalarlistpn" macro fixed (Zoltan Toth)
Typo:  Theorem GESD, missing "+" inserted deep into proof (Zoltan Toth)
Change:  Theorem SS, reordered conclusions (Zoltan Toth)
Change:  Theorem GESIS, new argument for invariance (Zoltan Toth)

New: Exercises from Chris Black, 123 in total, almost all with solutions:
SSLE: C30,C31,C32,C33,C34
RREF: M45
TSS: C21,C22,C23,C24,C25,C26,C27,C28
HSE: C21,C22,C23,C25,C26,C27
VO: C11,C12,C13,C14,C15,T5,T6,T7
SS: M10,M11,M12
MO: C10,C11,C12,C13,C14
MM: C21,C22,C23,C24,C25,C26,C30,C31,C32,C33,M30,M31
MISLE: C16,C17,C18,C19
MINM: C20,M10,M11,M15
CRS: C20
VS: M11,M12,M13,M14,M15,M20,M21
S: C15,C16,C17,T30,T31
LISS: C24,C25,C26
B: C10,C11,C12,C13,C14
D: C21,C22,C23,C35,C36,C37
DM: C21,C22,C23,C27,C28,C29,C30,M10,N11,M15,M16
EE: C10,C11,C12,C23,C24,C25,C26,C27
LT: C16,C40,C41,C42,C43
ILT: C26,C27,C28,C29,C30,C31,C32,C33
SLT: C23,C24,C26,C27,C28,C29,C30
IVLT: C25


v2.02  2008/11/19
~~~~~~~~~~~~~
Typo:  Proof of Theorem RREFU, fixed [R]_{k,d_l} subscript (Niall Davidson)
Typo:  Example CNS2 (Section HSE), augmented matrix needs column of zeros (Cicero Vargas)
Typo:  Subsection FS.EEF, very end, augmented matrix [A|x] corrected to [A|y] (David Braithwaite)
Typo:  Proof of Theorem UMCOB, inner product equals 0 (not 1) in beginning (Bryan Smith)
Typos:  117 typos and minor edits (Minh Van Nguyen)
Edits:  Various edits and typos (Bryan Smith)
Edit:  Theorem ETM, removed unnecessary eigenvector (David Braithwaite)
Edit:  Theorem DEC, i/j subscript fixed in proof
Change:  Solution MM.T41 rewritten, no longer depends on Theorem NI (David Braithwaite)
Change:  Theorem DT, induction step made explicit (David Braithwaite)

v2.01  2008/09/10
~~~~~~~~~~~~~
New:  Another solution for Exercise SSLE.C52(David Braithwaite)
New:  Computation Notes for SAGE:  RR (Row Reduce), LS (Linear Solve), VLC (Vector Linear Combinations)
Change:  Theorem VFSLS, bad subscripts in paragraph "Rearranging.." (David Braithwaite)
Change:  Theorem VFSLS, proof totally rewritten, includes correction above
Change:  Exercise SSLE.C51 clarified, new solution (Arnim Littek)
Edits:  Minor clean-up on SAGE Computation Notes
Typo:  Solution NM.C50, B renamed properly to E (George Garrett)
Typo:  Example NSDS (Section SS), -2 at top of z_1 at end (George Garrett)
Typo:  Solution SSLE.C52 had an extra 8 (David Braithwaite)
Typo:  Exercise TSS.T40, added "consistent" in hypothesis (David Braithwaite)
Typo:  Theorem MMCC, first justification in proof, reference corrected (Thomas Junier)
Typo:  SAGE output delimiters confusing XML translation (Harald Schilly)
Typo:  Exercise.SS.C44, Exercise.SS.C45, vector names fixed (George Garrett)
Typo:  Example RSSC4 renamed properly to Example RSC4 (Section LDS) (George Garrett)
Typo:  Variety of grammatical, spelling errors (George Garrett)
Typo:  Variety of grammatical, spelling errors (Arnim Littek)


v2.00  2008/07/16
~~~~~~~~~~~~~
New: Waldron Edition as print-on-demand
New: jsMath electronic version
New: Exercise MINM.M80
New: Solution SD.T16 (Steve Canfield)
New: Notation AME and Notation GME (eigenvalue multiplicities)
Change: Theorem IMR upgraded to iff (Sam Antoine)
Change: Theorem IMILT, simplified proof using Theorem IMR
Change: Figures are now Diagrams - avoids clash with TeX figure macros
Change: Preface is no longer an Invariant Text, to conform with strict open standards
Typo: Definition LSMR, Notation LSMR renamed correctly as MRLS
Typo: Theorem NOILT, removed duplicate "injective" (Steve Canfield)
Typo: Replace "gratis" by "gratuit" in Preface (Hubert Dupont)
Typo: Section NLT, first paragraph, geometric/algebraic multiplicty (Mariana Montiel)
Edit: Minor edits throughout Reading Questions, based on Spring 2008 course
Edit: Updated Preface


v1.35  2008/04/16
~~~~~~~~~~~~~
New: Computation Notes for SAGE, initiated by Steve Canfield
New: Exercises B.T51, PD.T33, MR.T20
New: Exercise B.T50 (which may become a Theorem)
Typo: Solution EE.C20, replaced 2 by -2 in eigenvalue 3 computation (Taylor Firman)
Typo: Solution EE.C22, replaced four 3i's by \sqrt{3}i (Matt Salter)
Bug: Source for v1.34 wouldn't TeX easily. Recalled. (Chris Black)


v1.34  2008/03/17
~~~~~~~~~~~~~
New: Expanded Theorem NPNT to include converse
New: Table at end of Subsection CRS.CSSE summarizing related theorems
New: Figure CSRST
Typo: Removed stray "=" from statement of Theorem EMP (Greg Palmer)
Typo: Removed "rank" and "nullity", Annotated Acronyms, Chapter M (Steve Canfield)
Edit: Minor edits in Chapter M, based on Spring 2008 course


v1.33  2008/03/06
~~~~~~~~~~~~~
Maintenance release for figures
  XML now contains figures
  Figures included in source tarball, XML tarball
  "List of Figures" still missing
Edit: Final revision of Fibonacci sequence, now Example FSCF (Section SD)


v1.32  2008/02/27
~~~~~~~~~~~~~
Figures now open-source via Python programs using PyX routines
  This infrastructure may change, experimental right now
  XML graphics import is not working
  Needs a "List of Figures"
  Not yet into source package, only in PDFs
New: Figures DTSLS, DLTA, DLTM, FTMR, FTMRA, MRCLT, GLT, ILT, NILT
Fixed excessive spacing following Proof Technique references
New: Use of Annotated Acronyms to Preface
New: Practicality and availability of hyperlinks to Preface
New: Exercises RREF.C33, NM.C50, NM.T30, LI.C32, LI.C33, LDS.C52, LISS.T50, O.T20, O.T30
New: Subsection SD.FS on Fibonacci sequences, needs some revision
Typo: Achetype C, second solution, x_2=7 (Betsy Kersey)
Typo: Example NSDS, portions of z_1 and z_3 reversed (Christina Roy)
Typo: Theorem TTMI, removed cruft from first half of proof (Christina Roy)
Typo: Example CSIP, carry -3+i through correctly (Matt Salter)
Edit: Example NRREF, named matrix E (from D) to avoid confusion with D, F as sets
Edit: Minor edits in Chapter R, concludes Fall 2007 course edits
Edit: Minor edits in Chapter SLE, Chapter V, based on Spring 2008 course
Edit: Streamlined proof of Theorem VRI
Edit: Definition of an Archetype is now from an open-source lexical database (WordNet)


v1.31  2008/02/02
~~~~~~~~~~~~~
Typo: Example VSP, b_1 corrected to a_1 (almost at the end)
Change:  Rewrote proof of Theorem RREFU
  Removed Subsection URREF from Section LC
  Moved Theorem RREFU to Section RREF
  Moved Techniques CD and U to precede
Change: Alternate proof of Theorem NMUS is now Exercise/Solution NM.T90
Edit: Clarified that Exercises C10-C19 in Section RREF are not designed to be worked by hand
Edit: Minor edits in Chapters VS, D, E, LT
Edit: Multiple edits in Section TSS
Edit: Removed unnecessary "m variables" from theorem hypotheses in Section TSS
Edit: Streamlined second half of proof for Theorem RCLS
Edit: Streamlined proof for Theorem SMZD
Edit: Streamlined proof for Theorem DRMM
New: Exercise SSLE.C51, SSLE.C52, RREF.T40


v1.30  2008/01/21
~~~~~~~~~~~~~
Production version for Spring 2008 UPS course
New: Annotated Acronyms: infrastructure is workable, but needs tuning
New: Annotated Acronyms for each of the 8 chapters in the core (Justin Platts)
New: Example CIVLT in Section IVLT, computing an inverse of a linear transformation
New: Exercise IVLT.M50
Change: Resolved acronym conflict for fields (commutativity, closure)
        Property ACCN renamed to CACN, Property MCCN renamed to CMCN
Change: Solution vector is now Definition SOLV, conflicted with Singular Values
Edit: Technique L, clarified comments on object-oriented programming (Clive Spriggs)
Edit: Theorem ISRN, removed "m equations" from hypothesis
Edit: Theorem EMMVP, made proof more reliant on standard unit vectors
Edit: Reworked statement of Theorem LTDB to be clearer, edited later applications
Edit: Significantly shortened proof of Theorem VRLT with new version of Theorem LTDB
Edit: Minor edits in Chapters SLE, V, M
Edit: Minor edits to Reading Questions
Edit: Fixed a few dangling cross-references
New: Standard Unit Vectors (Definition SUV) formalized as notation, e_i
Obsolete: Theorem CBOB (Justin Platts)
  As stated Theorem CBOB was likely false, proof was flawed
  Correct version melded into UMCOB, which is now an equivalence
  Some resulting adjustments in proof of Theorem PDM


v1.21  2007/11/21
~~~~~~~~~~~~~
New:  Exercise RREF.C19, TSS.T41, PEE.T50
Maintenance release to fix XML on-line version


v1.20  2007/08/29
~~~~~~~~~~~~~
Production version for Fall 2007 UPS course
New:  Exercises LI.T12, LI.T13, LT.T20, IVLT.T30
Typo: Solution MR.C42, employed inverse of representation (Will Swannack)
Concluded corrections from Spring 07 intro course (through CB)


v1.10
~~~~~~~~~~~~~
This version number skipped purposely


v1.09  2007/08/11
~~~~~~~~~~~~~
Obsolete:  Exercise LC.T30 (duplicates Theorem PSHS)
New:  Section HP, Hadamard product (by Elizabeth Million)
New:  Exercises MO.T14, LISS.T40, PD.T40
Typo:  Theorem PSMSR, forward implication, missing parentheses (Alex Paauwe)
Typo:  Example SS6W, made S really 10 digits long by adding a leading zero (Elizabeth Million)
Typo:  Section SAS, 4th paragraph, "choose  m-1  coefficients" (Elizabeth Million)
Typo:  Theorem DRCMA, second line of proof, remove row  t  of  B  (Tim Zitzer)
Typo:  Solution LT.C30, switched roles of X_2, x_3 (Celia Ozereko)
Typo:  Theorem ENLT, added "nilpotent" to hypothesis (Andrew Tapay)
Typo:  Theorem PSHS, now zero vector, not zero scalar
Typo:  Example COV, matrices I, A, B confused (Dylan Poulsen)
Typo:  Theorem DEC, inserted sign changes (-1)^{i+j}
Change:  Moved Definition SUV from Section MISLE to Section O
Change:  Theorem SVD, fixed end of proof, reordered U and D (Tim Zitzer)
Change:  Theorem DLDS, proof reworked in a more consistent style
Change:  Theorem OSLI, proof reworked in a more consistent style
Change:  Theorem EMMVP, proof reworked in a more consistent style
Change:  Rewrote Solution PEE.T20
Change:  Solution LISS.T40 now appropriate to location
Change:  Example CROB4, basis justification changed (Will Swannack)


v1.08  2007/03/29
~~~~~~~~~~~~~
New:  Section VM, Vandermonde Matrix
New:  Section SAS, Sharing a Secret
New:  Section CF, Curve Fitting (in-progress)
Change: Moved Section PSM out of Matrix Decompositions chapter
Typo:  Corrected typo in Solution T.T30 (Andy Zimmer)
Typo:  LISS.SS, color mixing analogy, changed "yellow" to "green" (Tate Urio)
Typo:  Theorem COB, set T relabeled correctly to B (proof improved also)


v1.07  2007/03/14
~~~~~~~~~~~~~
New:  Section SR, Square Root
New:  Section POD, Polar Decomposition
New:  Section SVD, Singular Value Decomposition
New:  Added discussion of unitary matrices as isometries (Section OD)
New:  Exercise PEE.T22
Change:  Renamed Theorem GSP as Theorem GSPCV  (Gram-Schmidt Procedure)
Change:  Relabeled unitary matrices (from Q to U) in Section MINM
Section T, Trace (nee Section TM) in draft form
Chapter MD, Matrix Decompositions, outline is complete, all sections in draft form


v1.06  2007/03/08
~~~~~~~~~~~~~
New:  Section PSM, Positive Semi-Definite Matrices
New:  Section TM, Trace of a Matrix (by Andy Zimmer)
New:  Theorem UMCOB in Section B, Theorem CBOB in Section CB
          (Unitary matrices and orthonormal bases)
Typo:  Example JCF10, removed extraneous identity linear transformations in matrix representations
Typo:  Definition JCF, corrected last two portions  (Kali Joseph)
Obsolete:  Theorem VAC, Theorem CSSM, Theorem CVSM of Section VS never referenced
                Removed and converted to Exercise VS.T21, VS.T22, VS.T23
Correction:  Removed duplicate version of Theorem UTMR (Section JCF)

v1.05  2007/02/27
~~~~~~~~~~~~~
Change:  Definition A (adjoint) moved into Section MO in new Subsection A
Change:  Definition HM (Hermitian) moved into Section MM
New:  Theorem CCM, Theorem AMA, Theorem AMSM, Theorem AA in Section MO
    Basic results about adjoints and Hermitian matrices
New:  Theorem MMAD, Theorem AIP, Theorem MMIP in Section MM
     Basic results relating matrix multiplication, adjoints, inner products
New:  Theorem OBNM (Section OD), orthonormal basis of eigenvectors for a normal matrix
Upgrade:  Streamlined proof of Theorem HMRE (Section PEE)
Upgrade:  Streamlined proof of Theorem HMOE (Section PEE)
Obsolete:  \adj  macro expunged in favor of  \adjoint
Typo: Reading question #3 in MINM, "orthogonal" corrected to "unitary"
Typo: Proof of Theorem RREFU, last paragraph,
  two subscripts corrected to read "except that b_k has a one in location d_k"  (Bryan Smith)

v1.04  2007/02/15
~~~~~~~~~~~~~
New:  Section OD, Orthonormal Diagonalization
   Logical structure is complete, needs examples and editing
New:  Example LTRGE in Section IS
New:  More detailed proofs of Theorem CVRA and Theorem CRSM (Section O)
Typo: Theorem IPVA, added comma to vector list in statement (Celia Ozereko)

v1.03  2007/02/01
~~~~~~~~~~~~~
New:  Section TD in draft form
New:  Exercises RREF.C17,C18,C32; TSS.M56,M57,T40;  HSE.C31;  NM.M30
Typo:  SSLE.SOL.C50 changed  c>2  to  c>1  (Celia Ozereko)
Addition:  Reworded Definitions CVE, CVA, CVSM in Section VO to include C^m explicitly (Kyle Morril)
Change:  Adjoint of a matrix notation is now a superscript star, changes only one occurence
Change:  Subsection SD.OD (Orthonormal Diagonalization) downgraded to a comment
Edit:  Minor editing in Section MINM (mostly source-level changes)

v1.02  2007/01/25
~~~~~~~~~~~~~
New:  Section JCF essentially complete, now a draft
New:  Section ROD in draft form
New:  Solution to MR.T80
New:  Example JCF10 in Section JCF
Typo:  Reference in Exercise MR.T80 fixed to read "Theorem EMP"
Typo:  Commutative diagram after Example MR.MPMR
          basis on final matrix representation now D (not C)  (Tim Zitzer)
Typo:  HSE.SOL.T10, implications reversed  (Tim Zitzer)

v1.01  2007/01/18
~~~~~~~~~~~~~
Completed:  Section NLT, Nilpotent Linear Transformations (now a draft)
New: Section IS, Invariant Subspaces  (now a draft)
New: Section JCF, Jordan Canonical Form (nearly complete)
New: Section F, Fields (first Topics section)
New: Subsection DS in Section PD
   especially to support theorems in Section NLT
   six or so new theorems in this section
New:  Minor updates to reading questions, clarifying questions' intent
New:  Exercise PD.M50
New:  Four new math macros in fcla-math.sty
   \geneigenspace  for generalized eigenspaces
   \restrict  for restrictions of linear transformations
   \indx  for the index of an eigenvalue
   \Z  for blackboard bold Z, the integers
Typo: EE.SOL.C19 - Fixed sign on constant term of char poly (Jessica Olsen)
Change:  Example IS (Section SSLE), replaced  beta_3, beta_4  by  a, b
Obsolete:  Theorem EB (Section PD), effectively replaced by Theorem DSFOS

v1.00  2006/12/11
~~~~~~~~~~~~~
Version 1.00 release  ;-)
Section NLT in-progress, not included in major release (see 0.94/1.01)
Change Log entries now more comprehensive

v0.94  2006/12/09
~~~~~~~~~~~~~
New exercises:  IVLT.T05, MR.C10
Many changes in formatting and work on production script
Refined sections in Chapter SLE with additional subsection headings
First XML production version
Version 1.0 release candidate

v0.93  2006/11/22
~~~~~~~~~~~~~
Commented out commutative diagrams in XML version
XML version ready for regular production
Got "linear system" notation right
New Theorem EB, Definition DS in Section PD
Expanded to two screen formats

v0.92  2006/11/16
~~~~~~~~~~~~~
XML characters working without PNG images
Customization switches rationalized, expanded
Eigenspaces now written with calligraphic E
New exercises:  PD.T05
New Theorem PSSD in Section PD
More new material in Section NLT


v0.91  2006/11/09
~~~~~~~~~~~~~
Edits in Chapters D, E
Retitled Theorem DMLE to DMFE (at Paul Wicks' suggestion)
Restyled the proof of Theorem EDELI
Began work on Jordan canonical form with Section NLT


v0.90
~~~~~~~~~~~~~
This version number skipped purposely


v0.89  2006/11/02
~~~~~~~~~~~~~
Lots of macro work to make XML version possible
Brought revised  fcla.tex,  fcla-developer.sty  into main tree
Renamed all *.tex files with acronym basenames to upper-case versions
New Exercise D.C40, PD.T10
Edits in Chapter VS
Orthogonal matrices properly renamed as unitary matrices
  Subsection OM to UM, Definition OM to UM, Theorem COMOS to CUMOS
  Example OM3 to UM3, Example OPM to UPM
Renamed \adjoint convenience macro as \adj
Created new \adjoint for notation purposes only
Finished Section SET
Added Theorem PCNA to Section CNO for subsequent references
All major content holes plugged in preparation for version 1.0  ;-)
Acronyms adjusted for Equality/Entry conflicts for vectors and matrices


v0.88  2006/10/19
~~~~~~~~~~~~~
Example PSNS renamed (correctly) as PSHS
New Exercises MM.T52, MISLE.C42, CRS.C34,C35, FS.C26
Moved matrix and vector notation for systems from Section HSE to Section RREF
Subsumed Definitions ZR, LO, PC and Notation RREFA into Definition RREF
Eliminated  notation  environment, since none remain
NonSingular acronym cleanup
  Replaced occurences of NS=NonSingular, generally with NM=Nonsingular Matrix
  Section NSM to NM, Section MINSM to MINM
  Subsections BNSM, CSNSM, LINSM, NSM, NSMI, RNNSM
  Theorem CINSM, CNSMB, NSI, NSLIC, NSRRI, NSTNS,
                RNNSM, SNSCM, CSNSM, NSMUS, NSMEx
  Example NS, NSNS, NSRR
\frontsection macro obsolete
GFDL to an Appendix
Contributor list handled by tocloft package
Computation notes infrastructure reworked
   Inline as environments
   Appendix with subsections
   User-controllable:  appendix/inline, choice of devices
Proof Techniques
   Now in appendix, or inline throughout text, switchable
\includesection macro now obsolete


v0.87  2006/10/12
~~~~~~~~~~~~~
Chapter M edits
Macro cleanup before XML/MathML additions


v0.86  2006/10/05
~~~~~~~~~~~~~
Archetype work
  New Archetypes: linear transformations W and X
  Provided full details on Archetypes S through X
  New Exercise IVLT.C10
  Refactored some archetype macros
  Formatted archetypes at the section level, fixed PDF bookmarks
  Reserved archetypes Y and Z for canonical form examples to come
  Created archetype summary supplement, added to distributions
  Archetypes now reasonably complete


v0.85  2006/09/28
~~~~~~~~~~~~~
New Section SET on sets
New Exercises SS.C50, LI.T15, LI.T50, LDS.C55
Definition ES relabeled as Definition ESYS
Proof Technique SE subsumed by Definition SE  (set equality)
Proof Technique SN absorbed into Section SET
Upgraded \chap macro to allow for appendices at same level
Renamed Chapter A (Archetypes) as an Appendix
Removed Chapter P (Preliminaries) from Topics part
New Appendix P (complex, numbers and sets)
Moved Proof Techniques out of running text, into Appendix PT
Started exporting Computation Notes to their own appendix
Lots of refactoring in sectioning macros
Stopped posting (nearly useless)  bugs.txt  file on website


v0.84  2006/09/21
~~~~~~~~~~~~~
Abandoned  ntheorem  package for environments and lists
Incorporated LaTeX \newenvironment to replace ntheorem
Incorporated  tocloft  package to replace ntheorem
Began using TeX4ht to produce XML/MathML output
New Example:  LIBNS in Section LI
New Example:  DRO in Section PDM
New Exercises:  PDM.T15, T20, T25
Polished the proof of Theorem BNS
Corrected RREF pseudo-code (after Theorem REMEF)
Three new reading questions in Chapter D
Expansion/Revision of Chapter D complete
New Mathematica Computation Notes:
   NS  (Null Space) in Section SS
   VFSS (Vector Form of Solution Set) in Section SS
Brought  flashcard  production in line with new environments
Broke out chapter introductions into own files
Added \allowdisplaybreaks to preamble, 30 page reduction


v0.83  2006/09/14
~~~~~~~~~~~~~
Added Exercises  SSLE.C50, NSM.T10
"Chapter" string into chapter headings
Corrected acronym: Theorem ESMHE is now Theorem EMHE
New Proof Techniques, placeholder references replaced
  Induction (I)
  Contradiction (CD)
  Lemmas and Corollaries (LC)
  Negations (N)


v0.82  2006/09/07
~~~~~~~~~~~~~
Polished Section RREF, reformatted row operations examples
New Example FDV in Section TSS
Wrote new Section PDM for Chapter D
  Many new theorems, a few examples, etc
Relocated following from Section DM to Section PDM
   Theorem SMZD, Example ZNDAB, Theorem NSME7, Theorem DRMM
Subsection PD of Section D is obsolete


v0.81  2006/08/31
~~~~~~~~~~~~~
Examples MIAK, CMIAK renamed as MI and CMI
   (now use a matrix different from Archetype K)
Reworking Chapter D, Determinants
   Added new Subsection on elementary matrices
   Changed notation for submatrices
   Removed definitions of minors and cofactors (MIM, CIM), and Example MC
   Obsolete:  \minor, \cofactor
   Several big proofs about determinants finally provided
   Theorem DERC decomposed to Theorem DER and Theorem DEC
   Planning new section with properties of determinants
Adjusted the end of Example IS (Section SSLE)
Typos, etc fixed in Sections WILA, SSLE


v0.80  2006/08/22
~~~~~~~~~~~~~
Renamed Subsection B.BRS as B.BSCV
Edits in Section B, D, PD
New Subsection PD.DFS
New Theorem DFS in Section PD
New reading question in Section PD
New Exercises B.C40
New Solution B.M20


v0.75  2006/04/06
~~~~~~~~~~~~~
Typo fixups in Chapters V, M, D, E
New Exercise PEE.T30


v0.74  2006/02/23
~~~~~~~~~~~~~
Rewrote Theorem PWSMS as the contrapositive, renamed as NPNT
New Exercises DM.T10, CRS.T45


v0.73  2006/02/16
~~~~~~~~~~~~~
Typo fixups in Chapters SLE and V
Changed acronym for Theorem ICRN to ISRN (Section TSS)
Overhauled proof of Theorem REMEF


v0.72  2006/01/26
~~~~~~~~~~~~~
Reviewed Section S, updated reading questions
New Examples LIC, SSC (Section LISS); BC (Section B); DC (Section B)
New Exercises LISS.C23, C42, B.C80
Example SSM22 reworked (Section LISS), changes reflected in Example BSM22 (Section B)
Completed reading questions for Section LISS


v0.71  2006/01/19
~~~~~~~~~~~~~
Began major reorganization of portions of Chapter VS
   New Section LISS, built from Subsections B.LI, B.SS, B.VR
   Subsection PD.OBC moved to Section B
   Improvements to Sections B, D, PD planned
New exercises:  SSLE.M11, M12, M13


v0.70  2006/01/05
~~~~~~~~~~~~~
Production version for Spring 2006 UPS course
Revised Preface
Fixed busted cross-references
Renamed Theorem RSS as Theorem SS (Section LDS)
Fixed Example MRCM
EXPERIMENTAL:  Span notation converted to angle brackets (nee Sp( ))
New exercise:  SSLE.M10

v0.65  2005/12/15
~~~~~~~~~~~~~
New exercises:  MR.C22, C25, C42, C52;  CB.41
Improvements to Theorem KNSI and Theorem RCSI (Section MR)
Chapter R: Typos and polishing


v0.64  2005/12/01
~~~~~~~~~~~~~
New proof:  Theorem LTTZZ (from Mark Shoemaker)
New exercises:  ILT.C20; SLT.C22; IVLT.C20, C21, M31
Typos, etc in Chapter LT


v0.63  2005/11/17
~~~~~~~~~~~~~
New examples:  ELTT, CELT (Section CB)
Renamed Theorem BCSOC as Theorem BCS
New exercises:  DM.C24; EE.C19, T20; PEE.T10; SD.C22


v0.62  2005/11/10
~~~~~~~~~~~~~
Fixed up Theorem EDELI (Section PEE)
Fixed up Exercises ILT.T20, SLT.T20
Typos, etc in Chapters D & E
New example:  MRBE (Section MR)
New theorems:  IMILT, NSME9 (Section MR)
New exercises:  MR.T60


v0.61  2005/11/03
~~~~~~~~~~~~~
Significantly simplified proof of Theorem RMRT
New exercises:  B.C22, C41; D.C30, C31; CB.C20, C21, T15
New examples in Section CB:  ELTBM, ELTBP, CBP, CBCV, MRCM


v0.60
~~~~~~~~~~~~~
This version number skipped purposely


v0.59  2005/10/27
~~~~~~~~~~~~~
Typos in Chapter VS fixed
Theorem LNSMS (Section S)
Reformatted proof of Theorem REMRS
New exercises:  MR.C21, C41, C50, C51, M20; CB.C40;


v0.58  2005/10/20
~~~~~~~~~~~~~
Polished Section VS, de-emphasized "axioms"
Improved proof of Theorem CSNSM (Section MINSM)
Improved proof of Theorem TSS (Section S)
Section FS: New Example LNS, warning on row-reducing to a column space
Section FS: full-rank discussion for minimal L
New exercises:  RREF.T21; CRS.M21; FS.C21, M50, M51
New exercises:  MISLE.C41; CRS.C31; FS.C25
New exercises:  LT.C26, C31; ILT.C40, T20; SLT.C40, T15; IVLT.M30


v0.57  2005/10/13
~~~~~~~~~~~~~
Proof for Theorem FS (Section FS)
Minor typos fixed in Section FS


v0.56  2005/10/06
~~~~~~~~~~~~~
Polished proof of Theorem OSIS (Section MINSM)
Retitled Definition TSS as Definition TSVS
Rewrote Theorem PSPHS, allows section move below
Moved Subsection PSHS from Section MM to Section LC
Internal commands obsolete:  \fileinfo, \titlingdotted
New exercises:  SS.T21, T22; MM.T31, T32, T51; MINSM.T12;
New exercises:  S.C21, T20;  B.C21, C40;  D.M21


v0.55  2005/09/29
~~~~~~~~~~~~~
Polished Sections MO, MM, MISLE, MINSM
Internal commands obsolete: \vectorcomponents
Added Theorem MCT to Section MO
Proof of Theorem SLSLC rewritten
Proofs of SLEMM and EMP adjusted with new notation
Moved exercise:  VO.T30 becomes LC.T30 with new solution
New exercises:  VO.T30; SS.C44, C45; LI.C25, C31; LDS.C51, T40


v0.54  2005/09/22
~~~~~~~~~~~~~
Fixed missing "=" in statement of Theorem EMP
Fixed Spring 2005 typos in Chapter M
\archetyperef (source level command) is now obsolete
New exercises:  LC.C41; MO.T13, T17, T18, M20-M25; CRS.T40, T41
New exercises:  RREF.C15, C16, C31;  TSS.M53; HSE.C30;  NSM.C33, M52
New exercises:  DM.C26;  EE.C22;  PEE.T20; SD.C21, T17


v0.53  2005/09/15
~~~~~~~~~~~~~
New proof of Theorem VFSLS completed (Section LC)
Polished Theorem SSNS (statement and proof, u vectors are now z vectors)
Reworked, standardized, expanded Notation items, more to add
Fixed Fall 2005 typos in Chapter V
New Definition RR ("row-reduce", Section RREF)
New Example VFS (Section LC)
New Example ABS (Section SS)
New Example NSDS (Section SS)
Expanded Exercise SS.C22
Expanded the proof of Property DSAC (Section VO)
New exercises:  O.T10,T11; LC.M11; SS.C23,T20


v0.52  2005/09/08
~~~~~~~~~~~~~
Fixed Fall 2005 typos in Chapter SLE
Slightly restated Theorem VFSLS
New Proof Technique PI (in Section VO)
New proof of Theorem VFSLS (half-done)
Polished Sections VO, LC
New exercises:  MISLE.C28,C40; MINSM.M20; CRS.C33,M10; FS.C60
Moved exercise: CRS.C35 to FS.C61
Removed exercise: TSS.M53


v0.51  2005/09/01
~~~~~~~~~~~~~
Polished Chapter SLE
Moved  \matrixentry  notation to Section RREF (now earlier)
Employed \matrixentry notation in Chapters SLE, M (Chapter V to do later)
Added Examples CNS1, CNS2 to the end of HSE
New exercises: SS.C42,C43,T10; LI.C23,C24,C30; LDS.C20


v0.50  2005/08/28
~~~~~~~~~~~~~
Production version for Fall 2005 UPS course
Section FS nearly complete, needs main proof
Converted null spaces of linear transformations to kernels


v0.42  2005/08/24
~~~~~~~~~~~~~
Reorganized customization switches
Polished all reading questions with AY 2004-05 class feedback
Fixed Example NSVMR
Added Example RVMR
Renamed Section SSLE to SSSLE (removed "simultaneous")
Renamed Definition SSLE to SLE (removed "simultaneous")

3 major rearrangements:

1.  New section, LDS, added after LI
     Moved Subsection LI.LDSS into Section LDS
     Example COC moved from Section LI to Section LDS, renamed as COV

2.  Renamed range of a matrix as column space of a matrix
     Merged Sections RM and RSM into single new section, CRS

3.  Initiated a new section, FS, at end of Chapter M (needs renovating)


v0.41  2005/04/21
~~~~~~~~~~~~~
Polished Section MR
Several large examples added to Section MR
Section CB left in unfinished state


v0.40  2005/04/14
~~~~~~~~~~~~~
Polished Section VR
Added two large examples to Section MR
Added several exercises to Chapter R


v0.39  2005/04/07
~~~~~~~~~~~~~
Polished IVLT
Updated Archetypes table


v0.38  2005/03/24
~~~~~~~~~~~~~
Improvements to Sections LT, ILT, SLT (more needed)
New Example BRLT


v0.37  2005/03/20
~~~~~~~~~~~~~
Polished Sections D, PD, DM, EE, PEE, SD
Additional exercises to D, PD, DM, EE, SD
Cleaned up Archetypes M through R
New Theorem EDYES
Proof for Theorem DCP
Theorem SLTS reworked to become Theorem SSRLT


v0.36  2005/02/24
~~~~~~~~~~~~~
Polished Sections S, B
Additional exercises added to S, B
Version number to bottom corner of each page
Computation Notes for the transpose of a matrix (TI-86, Mathematica)
Improved the polynomials in Example SSP
Reworked proof of Theorem RMRST
New Problem VS.M10


v0.35  2005/02/17
~~~~~~~~~~~~~
Polished Sections MISLE, MINSM, VS
Additional exercises added to MISLE, MINSM, VS
More detail in proof of Theorem TTMI
Replaced freebie reading question in MINSM
Tagged axioms of Definition VS with properties
Restyled proofs in Subsection VS.VSP


v0.34  2005/02/10
~~~~~~~~~~~~~
Polished Sections RM, RSM, MM
New Example MRM early in Section RM
Additional Exercises in RM, RSM, MM


v0.33  2005/02/03
~~~~~~~~~~~~~
Polished sections LI, O, MO
Three new examples in Subsection LI.LIV
New exercises in Sections LI, O
Added reading questions to Section O
Tagged the 10 vector space properties of matrices in Theorem VSPM
Split Theorem TASM into Theorem TMA and Theorem TMSM
Added theorems about matrix conjugation and matrix operations
Added Example MBC to Section MM
Added exercises to Chapter SLE from chapter exam


v0.32  2005/01/27
~~~~~~~~~~~~~
Polished sections VO, LC and SS
Added exercises to sections VO, Lc and SS
New Exercise HSE.T10
Overhauled Theorem VSPCV to tag 10 axiom-like properties
New Example SSNS right after Theorem SSNS (Section SS)

v0.31  2005/01/20
~~~~~~~~~~~~~
Additions to exercises throughout Chapter SLE
Fixed top row in Example SAE
Polishing throughout Chapter SLE

v0.30  2005/01/17
~~~~~~~~~~~~~
Production version for Spring 2005 UPS course
Updated Preface
GPL'ed sources
Calligraphic letters for range, null space, etc.
Moved in Reading Questions
Moved Subsection SS.VFSS (vector form of solutions) into Section LC
Modified Theorem BNS, so paired references to Theorem SSNS are unnecessary
Examples' acronyms no longer have "dotted" section name prefix
Abandoned use of the term "Corollary"
Split out Theorem TT from Theorem TASM
Many dead and conflicting references fixed
Chapters LT and R left to be overhauled later
Eliinated links to solutions when they did not really exist
Theorem NSMUS gets new proof on one half

v0.25  2005/01/13
~~~~~~~~~~~~~
Maintenance release, changes listed in v0.30

v0.24  2004/12/31
~~~~~~~~~~~~~
Maintenance release, changes listed in v0.30

New Section MR (without examples)
New Section CB (without examples)
Completed content for UPS course

v0.22  2004/11/18
~~~~~~~~~~~~~
New Section VR
Outlined theorems for Section MR

v0.21  2004/11/11
~~~~~~~~~~~~~
Completed proof of Theorem ME
New Section IVLT
Added commutative diagrams after Definition LT

v0.20
~~~~~~~~~~~~~
This version number skipped purposely

v0.19  2004/11/04
~~~~~~~~~~~~~
Sections ILT, SLT nearly complete
Section VR underway
Began experiments with TeX4ht, aiming at MathML version
Archetypes S to W initiated (linear transformations between abstract vsps)
A few homework problems to Chapters M and VS

v0.18  2004/10/28
~~~~~~~~~~~~~
New Sections ILT and SLT both half-complete
C^m linear transformations added to Archetypes (M through R)
Lots of housecleaning in Chapters D & E

v0.17  2004/10/21
~~~~~~~~~~~~~
New sections:  EE, PEE, SD (all of Chapter E)
Added Theorem DT to Section DM
Added Example DM.ZNDAB (zero/nonzero determinant)
Added Theorem MIMI to Section MISLE
Added eigenvalue information to Archetypes A, B, F, K, L

v0.16  2004/10/07
~~~~~~~~~~~~~
New Sections DM, LT
Moved out complex number arithmetic to a "preliminary" topic
Instituted Parts (Core, Topics, Applications)
Gram-Schmidt to Section O (Orthogonality)
Inserted section headings into theorem, definition lists, etc.

v0.15  2004/09/29
~~~~~~~~~~~~~
New Section PD
Integrated new material on conjugates, inner products to properties of vectors and matrices
Orthogonal matrices added to Section MINSM
Inner product as matrix multiplication to Section MM

v0.14  2004/09/22
~~~~~~~~~~~~~
New Section O, Section D
Finalized flash cards
Began adding exercises
Renamed Theorem SST as Theorem SS
Removed the new Definition SUVCM from Section B
Fixed dysfunctional links to frontmatter
Replaced \setvert macro with \setparts{}{}, eliminated \setvert
Rearranged customization switches
Added A4 paper, screen, and "electric" paper sizes
Contributors and exercises infrastructure working


v0.13  2004/09/16
~~~~~~~~~~~~~
Added Section B
Automated production of flash cards
Instituted Section O in Chapter V
Renamed Example RM.ROC as RM.ROCD
Renamed Definition RS as RSM
Renamed Sections ROM, RSOM, MOM as RM, RSM, MM
New discussion about the definition of a nonsingular matrix
Began adding computation notes for TI-83 (courtesy of Doug Phelps)


v0.12  2004/09/09
~~~~~~~~~~~~~
Added new Section S
Fixed typos in sections TSS, HSE
Removed "french" links (screwy font for references) in print versions
Allowed for non-existent computation notes
Added Linear Solve computation note
Modified Example TSS.RREFN (added ninth column)
Example TSS.OSGM renamed to TSS.OSGMD
Example TSS.ISS renamed to TSS.ISSI
Notation MEN renamed as Notation ME
Corrected name of Theorem RMSRT, now Theorem RMRST
Definition TS renamed to Definition TSHSE


v0.11  2004/09/02
~~~~~~~~~~~~~
Added new Section VS.
Subsection MISLE.PMI named properly.
Fixed typos in sections WILA, SSSLE, RREF.
Started adding computation notes:
  Matrix entry, row reducing for Mathematica, TI-86.
Cleaned up reduced row-echelon form and procedure for obtaining it.
Renamed Definition SSV as SSCV for consistency.


v0.10  2004/07/27
~~~~~~~~~~~~~
First released version.
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