From 4e26d0c602260a30a5b78743f93b4f76e14ea864 Mon Sep 17 00:00:00 2001 From: James Geddes Date: Thu, 18 Jul 2024 11:28:43 +0100 Subject: [PATCH] Add beginning of answers to Axler 5A. --- exercises/axler-5a.org | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100644 exercises/axler-5a.org diff --git a/exercises/axler-5a.org b/exercises/axler-5a.org new file mode 100644 index 0000000..546c51e --- /dev/null +++ b/exercises/axler-5a.org @@ -0,0 +1,16 @@ +#+title: Questions from Axler 5a + +3,8,13,35 + +* Question 3 + +Suppose \( T \in \mathcal{L}(V)\). Prove that the intersection of every +collection of subspaces of \(V\) invariant under \(T\) is invariant +under \(T\). + +** Answer + +Let \(U_\lambda\) (\(\lambda\in\Lambda\)) be some family of subspaces such that each \(U_\lambda\) +is invariant under \(T\). + +