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I suspect that the following matrix inequality is well known, but I can't find a reference or proof: Given $n \times n$ symmetric matrices $A,B$ such that $I_n \leq A,B$, is the following true? $${...

This question is in part related to a question that I have already posed. Say I have two symmetric positive definite matrices and their respective Cholesky decompositions $\mathbf{A} = \mathbf{L}_A \...

Let us consider the space $M_n(\mathbb{C})$. By a unitary matrix $U=(u_{ij})$ we mean that $U^{-1}=(\overline{u_{ji}})$. Q. Let $U$ be a unitary matrix. I am looking for the pairs of matrices $(D,A)$ ...

I realize this question is not high level but I have posted it on Math Stackexchange: Stackexchange question and have received some upvotes but no answers or comments, so I am trying here. I will need ...

Let $A \in \mathbb{R}^{n \times n}$ be a normalized non-strict column diagonally dominant matrix, that is: $$a_{j,j} = \sum_{i \ne j} \left|a_{i,j}\right|$$ where $0 \le a_{j,j} \le 1$ and $-1 \le ...