3 problems

Let $A$ and $B$ be complex $n\times n$ matrices. Write the singular values of $A$ as $\sigma_1\geq\dots\geq\sigma_n\geq0$, and define … For $1\leq p<\infty$, let…

Let $A$ be a complex $n\times n$ matrix with singular values … Let $\Sigma_\uparrow(A)=\operatorname{diag}(\sigma_1,\dots,\sigma_n)$ and…

Let $A$ and $B$ be complex $n\times n$ matrices, and for $1\leq p<\infty$ define $\|A\|_p=(\operatorname{Tr}|A|^p)^{1/p}$, where $|A|=(A^*A)^{1/2}$. The matrix Hanner inequality is…