All Questions

I am investigating a function defined in terms of the singular values of matrices. Initially, I simplified the problem by focusing on the eigenvalues of $2 \times 2$ Hermitian, positive-definite ...

Let $A,B\geq0$ be positive semidefinite matrices of arbitrary size $n\times n$. Denote by $\alpha$ and $\beta$ their largest eigenvalues. It is well-known that the eigenvalues of the expression $AB +...

Let $A, B$ be Hermitian matrices. Does the following hold? $$\det(A^{2}+B^{2}+|AB+BA|)\leq \det(A^{2}+B^{2}+|AB|+|BA|)$$ As usual, $|X|=(X^*X)^{1/2}$. Clearly, quantities on both sides are no less ...

While mimicking the union bound in quantum systems, we land on the following conjecture but don't know how to prove this. Given any complex-valued $n\times m$ matrix $A$. A sub-matrix of $A$ is ...

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? $${...