 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[True.] The <symmetric and antisymmetric parts of a matrix> are, in <Einstein summation convention>,
$$
S_{ij}=\frac{M_{ij}+M_{ji}}2,\qquad A_{ij}=\frac{M_{ij}-M_{ji}}2.
$$
They satisfy $S_{ji}=S_{ij}$, $A_{ji}=-A_{ij}$ and $S_{ij}+A_{ij}=M_{ij}$. This works over the real or complex numbers; it uses division by two.

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