3 problems

Let $n$ be a positive integer, $A_1,dots, A_n$ be symmetric positive semidefinite matrices, and let $\lVert\,\cdot\,\rVert$ be the spectral norm. For $m\leq n$, compare the average…

Let $A_1,\dots,A_n$ be positive semidefinite matrices, and let $\lVert\,\cdot\,\rVert$ denote the matrix norm used in the conjecture. For ordered products of length $m$, distinguis…

Let $m\leq n\in\mathbb{N}$ and let $A_1,\dots,A_n$ be positive semidefinite matrices. Consider the normalized sum of spectral norms of all ordered products and the corresponding su…