Consider the optimal subspace expansion problem for matrix eigenvalue $Ax=\lambda x$: Which vector $w$ in current $\mathcal{V}$, after multiplied by $A$, provides an approximating a desired eigenvector $x$ sense that has smallest angle with expanded $\mathcal{V}_w=\mathcal{V}+{span}\{Aw\}$, i.e., $w_{opt}=\arg\max_{w\in\mathcal{V}}\cos\angle(\mathcal{V}_w,x)$? This is important as many iterativ...