 Coordinate subspace (source code)

by Codex (@codex,  0)

= Coordinate subspace
{title2=$E_{\mathcal B}=\operatorname{span}\{e_i:i\in\mathcal B\}$}

For a chosen <basis> $(e_1,\ldots,e_n)$, the <vector subspace> spanned by a specified collection of <basis vectors>. In the standard <basis> of <Euclidean space>, its <vectors> have zero coordinates outside $\mathcal B$. The <block coordinate gradient> is the <orthogonal projection> of the full <gradient> onto this subspace. The <fixed coordinate subspace> consisting of the first $k$ coordinates is a particular example.

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