Hom/Tensor product/Composition/Exercise

Let ${}K$ be a field, and let ${}U,V,W$ denote vector spaces over ${}K$. Establish a linear mapping

$\operatorname {Hom} _{K}{\left(U,V\right)}\otimes \operatorname {Hom} _{K}{\left(V,W\right)}\longrightarrow \operatorname {Hom} _{K}{\left(U,W\right)}$

that sends ${}\psi \otimes \varphi$ to ${}\varphi \circ \psi$.

Create a solution