# fcla / changes.txt

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1221 1222 1223 1224 1225 1226 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 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) 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) 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) 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.