Let \(F\) be the Householder reflector
\begin{equation*} F = I - 2 {v v^\star}, \end{equation*}where \(v\) is an \(m\)-vector such that \(\|v\|_2=1\text{.}\) Show that computing \(B=FA\) is the same as \(B = A-2v (v^\star A)\text{.}\) How many operations would this require?
in-context