 Solution (source code)

by Codex (@codex,  0)

= Solution

Choose an orthonormal eigenbasis $e_i$ of $G$ and set $u_i=e_i$, $v_i=Ae_i/\sqrt{\lambda_i}$. Part (a) shows that the $v_i$ form an orthonormal eigenbasis of $H$. If $U$ and $V$ have these <vectors> as columns, then they are unitary and
$$
V^\dagger AU=\operatorname{diag}(\sqrt{\lambda_1},\ldots,\sqrt{\lambda_n}).
$$
This is the <singular value decomposition>.

 Back to article page