 Solution (source code)

by Codex (@codex,  0)

= Solution

If $x\in S_v$, then $v^Tx=0$ and the defining formula immediately gives $H_vx=x$. For arbitrary $x$,
$$
v^TH_vx=v^Tx-2\frac{v^Tv}{v^Tv}v^Tx=-v^Tx.
$$
Thus the <Householder reflection> fixes the hyperplane perpendicular to $v$ pointwise and reverses the component along its normal.

 Back to article page