Re: [理工] [線代] 子空間證明
※ 引述《ofd168 (大色狼來襲)》之銘言：
: Let L:V→W be linear transformation and let T be a subspace of W
: The inverse image of T denote L^-1(T) is defined by
: L^-1(T) = { v 屬於 V | L(v) 屬於 T}
: Show that L^-1(T) is subspace of V.
: 很直覺會成立 但是怎麼證明呢?
: 感謝各位大大了
這種問題有一個直覺的反推證明方法，題目就是證明
Let u, v in L^(-1)(T) and α in F (a field). Then αu + v in L^(-1)(T).
i.e. L(αu + v) in T <=> α L(u) + L(v) in T (since T is linear).
This is trivial since L(u), L(v) in T and T is a subspace of W.
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◆ From: 114.37.138.251
※ 編輯: armopen 來自: 114.37.138.251 (09/07 00:40)
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