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I am reading Linear Algebra Done Right and want to prove that $L(V, W)$ is a vector space. I have read the solution here: Why the proof of closure under addition in Linear Map is $(T+S)(u+v)$ inst
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How to Prove a Set of Functions is Closed Under Addition (Example with functions s.t. f(0) = 0)
How to Prove a Set of Functions is Closed Under Addition (Example with functions s.t. f(0) = 0)