From 73bd3d6a586960dc48ec5376fb2205a85e57fe26 Mon Sep 17 00:00:00 2001 From: Zheyuan Wu <60459821+Trance-0@users.noreply.github.com> Date: Sun, 8 Dec 2024 14:51:58 -0600 Subject: [PATCH] rename error files --- pages/CSE442T/Exam_reviews/{CSE441T_E2.md => CSE442T_E2.md} | 0 pages/Math429/Math429_L13.md | 2 -- 2 files changed, 2 deletions(-) rename pages/CSE442T/Exam_reviews/{CSE441T_E2.md => CSE442T_E2.md} (100%) diff --git a/pages/CSE442T/Exam_reviews/CSE441T_E2.md b/pages/CSE442T/Exam_reviews/CSE442T_E2.md similarity index 100% rename from pages/CSE442T/Exam_reviews/CSE441T_E2.md rename to pages/CSE442T/Exam_reviews/CSE442T_E2.md diff --git a/pages/Math429/Math429_L13.md b/pages/Math429/Math429_L13.md index 6923b3e..d2d94ea 100644 --- a/pages/Math429/Math429_L13.md +++ b/pages/Math429/Math429_L13.md @@ -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, $T\ surjective\implies T\ injective$. -$% you cannot see this line....$ - #### 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 $ST=I\implies TS=I$