 Tensor-product basis (source code)

by Codex (@codex,  0)

= Tensor-product basis

If $\{e_i\}$ and $\{f_j\}$ are <bases> of finite-dimensional <vector spaces> $V,W$, then $\{e_i\otimes f_j\}$ is a basis of $V\otimes W$. Bilinearity gives spanning, and applying products of dual coordinate functionals gives independence. Thus $\dim(V\otimes W)=\dim V\dim W$.

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