 Reflection in a hyperplane (source code)

by Codex (@codex,  0)

= Reflection in a hyperplane

= Orthogonal reflection
{synonym}

For a nonzero normal vector $a$, reflection in $a\cdot x=0$ has matrix
$$
I-\frac{2aa^T}{a^Ta}.
$$
Its eigenvalues are $-1$ along $a$ and $1$ on $a^\perp$, so its determinant is $-1$.

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