 Multilinear map (source code)

by Codex (@codex,  0)

= Multilinear map
{wiki}

A <multilinear map> $F:V_1\times\cdots\times V_r\to W$ is a map between <vector spaces> that is linear in each argument when all other arguments are fixed. For example the evaluation $(\omega,v)\mapsto\omega(v)$ is bilinear, and the <determinant> is multilinear in its columns. The <universal property of a tensor product> replaces this separate linearity by a single <linear map> from $V_1\otimes\cdots\otimes V_r$.

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