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rename error files

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Zheyuan Wu
2024-12-08 14:51:58 -06:00
parent 6ffcf9e50d
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pages/CSE442T/Exam_reviews/CSE441T_E2.md → pages/CSE442T/Exam_reviews/CSE442T_E2.md
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pages/Math429/Math429_L13.md
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@@ -26,8 +26,6 @@ Suppose $T$ is injective, then $null\ T={0}$, i.e $dim(null\ T)=0$, since $dim\
If $T$ is surjective, then $dim\ range\ T=dim\ W$ but then $dim\ V=dim\ null\ T+dim\ W\implies dim\ null\ T=0$, so $T$ is injective, $T\ surjective\implies T\ injective$. If $T$ is surjective, then $dim\ range\ T=dim\ W$ but then $dim\ V=dim\ null\ T+dim\ W\implies dim\ null\ T=0$, so $T$ is injective, $T\ surjective\implies T\ injective$.
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#### Theorem 3.68 #### Theorem 3.68
Suppose $V,W$ finite dimensional $dim\ V=dim\ W$, then for $T\in\mathscr{L}(V,W)$ and $S\in \mathscr{L}(W,V)$, then $ST=I\implies TS=I$ Suppose $V,W$ finite dimensional $dim\ V=dim\ W$, then for $T\in\mathscr{L}(V,W)$ and $S\in \mathscr{L}(W,V)$, then $ST=I\implies TS=I$