2 problems

Let $\mathcal{H}$ be a complex separable Hilbert space, let $\mathcal{B}(\mathcal{H})$ be the algebra of bounded linear operators on $\mathcal{H}$, and let $\mathcal{I}$ be the set…

Let $Z$ be an invertible matrix with polar decomposition $Z=U_p\sqrt{Z^*Z}$, where $U_p$ is its unitary polar factor, and let $\operatorname{Log}$ denote a matrix logarithm. Let…