All Questions

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 perusing the Matrix norms section of Wikipedia, I came across this generalized version of Holder's inequality. $$ \|A\|_2^2 \leq \|A \|_1 \|A \|_\infty\,, $$ where, $$ \|A \|_p = \max_{\|x\|_p ...

Let $A,B$ be Hermitian matrices so that $0 \le A,B < I$ and also $(1-\varepsilon)(I-B)\le I - A \le (1+\varepsilon)(I-B)$. For every $t \in \mathbb{N}$, consider the matrix $A_{t} = \sum_{i=0}^{t}...

Let $A,B$ be two $n\times n$ matrices. Find a lower bound of the $p$-th Schatten norm $\|(A-B)(A-B)^\ast\|_{S_{p/2}}^{1/2}$ in terms of Schatten norm of $\|(AA^*+BB^*)\|_{S_q}$ for any relation ...