2 problems

Let $A$ be a Hermitian matrix, and let $\mathcal{X}$ and $\mathcal{Y}$ be subspaces of the same dimension, with orthonormal basis matrices $X$ and $Y$, respectively. Let…

Let $A\in\mathcal{H}(d)$ and let $\mathcal{X},\mathcal{Y}\subset\mathbb{C}^d$ be subspaces with $\dim(\mathcal{X})=\dim(\mathcal{Y})=k$. Let $\rho(X)$ and $\rho(Y)$ denote the comp…