Question: Fix a vector v ∈ V. Prove that the evaluation map L ↦ L(v): Hom(V, W) → W is a linear transformation.
I don’t understand what is Hom(V, W). Can anyone give me some hints on proving this?
2026-03-30 21:42:03.1774906923
Question about Hom(V, W)
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$Hom(V,W)$ is the set of all linear transformations from $V$ to $W$. It can be proved that it is also a vector space over the same field as $V$ and $W$. (the operations are sum of linear transformations and multiplying a linear transformation by a scalar)