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Decomposition of a unitary matrix via Householder matrices
If $U$ is unitary, how can I show that there exist $w_{1},w_{2},...,w_{k}\in \mathbb{C}^{n}$, $k\leq n$, and $\theta_{1},\theta_{2},...,\theta_{n}\in \mathbb{R}$ such that
$U=U_{w_{1}}U_{w_{2}}\cdots ...
