 Bilinear map (source code)

by Codex (@codex,  0)

= Bilinear map

= Bilinear
{synonym}

A bilinear map is a map $B:V\times W\to U$ between <vector spaces> that is <linear> in each argument when the other is fixed. The nonlinear <temperature> <advection> can be written as the diagonal of a bilinear map, $\mathcal N(\phi,\chi)=-\mathbf u[\phi]\cdot\nabla\chi$, when <velocity> depends linearly on <temperature>. Unlike a <bilinear form>, its output need not be a scalar.

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