All Questions

Let $A$ some square matrix with real entries. Take any norm $\|\cdot\|$ consistent with a vector norm. Gelfand's formula tells us that $\rho(A) = \lim_{n \rightarrow \infty} \|A^n\|^{1/n}$. Moreover, ...

I am wondering what are the best known relationship between $\|A\|_{2\rightarrow 2}$ and $\|A\|_{\infty\rightarrow 2}$ and how tight it is. E.g., the trivial result is that for matrix $A$ with ...

For any nonnegative semidefinite matrix $A$ and any matrix $B$, we have $$\mbox{tr} (AB) \le \mbox{tr} (A) \, \|B\|$$ where $\mbox{tr}(\cdot)$ is the trace and $\|\cdot\|$ is the operator norm. How ...

Let $M\in M_n(\mathbb C)$ be a $n\times n$ matrix over the complex field. It can be written uniquely as $M=H+A$, where $H=H^*$ denotes its Hermitian part and $A=-A^*$ its anti-Hermitian part. Its ...

I will use $\|\|_*$ to denote the nuclear norm (sum of singular values) and $\|\|_2$ to denote the operator norm / matrix 2-norm (largest singular value). Consider two positive definite $n \times n$ ...

Let's define the following subordinate norm of a $(NM \times NM)$ matrix A norm as follows \begin{eqnarray*} ||A||_{2,b} = \mathrm{max}_{x \in \mathbb{C}^{NM}} \left \{ \frac{||A x||_b}{||x||_2} \...