Re: [線代] 向量空間問題
※ 引述《vinsanity313 (喔!)》之銘言：
: 這是101年中央資工第12題的b選項，題目如下：
: V為一向量空間，X, Y為V的子集
: Let V^x denote the set of all mappings from X to V.
: Then V^x is a vector space.
Let V be a vector space over a field F
and let V^x = {f: f(x) in V for all x in X}.
First, you need to prove that (V,+) is an abelian group
where + is the function addition defined by
(f+g)(x) := f(x) + g(x) for all x in V.
We can define the additive identity h of V^x by
h(x) = 0 for all x in X, where 0 is the additive identity
of V. The remainder work is a lot of routines, we leave it to
you.
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