# Commits

committed 274ae6e

Theorem OSLI, "nozero" to "nonzero" (Anna Dovzhik)

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# File changes.txt

 Typo: Section LI, "in linearly independent" (Becky Hanscam)
 Typo: Example LDRN, use Theorem LIVRN as justification (Anna Dovzhik)
 Typo: Sage RLD, "nest" to "next" (Gavin Tranter)
+Typo: Theorem OSLI, "nozero" to "nonzero"  (Anna Dovzhik)


 v3.10 2013/08/20

# File src/section-O.xml

 <![CDATA[&&]]><acroref type="definition" acro="IP" />
 </alignmath></p>

-<p>Because $\vect{u}_i$ was assumed to be nozero, <acroref type="theorem" acro="PIP" /> says $\innerproduct{\vect{u}_i}{\vect{u}_i}$ is nonzero and thus $\alpha_i$ must be zero.  So we conclude that $\alpha_i=0$ for all $1\leq i\leq n$ in any relation of linear dependence on $S$.  But this says that $S$ is a linearly independent set since the only way to form a relation of linear dependence is the trivial way (<acroref type="definition" acro="LICV" />).  Boom!</p>
+<p>Because $\vect{u}_i$ was assumed to be nonzero, <acroref type="theorem" acro="PIP" /> says $\innerproduct{\vect{u}_i}{\vect{u}_i}$ is nonzero and thus $\alpha_i$ must be zero.  So we conclude that $\alpha_i=0$ for all $1\leq i\leq n$ in any relation of linear dependence on $S$.  But this says that $S$ is a linearly independent set since the only way to form a relation of linear dependence is the trivial way (<acroref type="definition" acro="LICV" />).  Boom!</p>

 </proof>
 </theorem>