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Let $A,B$ be two unitary matrices in $U(n)$, and $\|\cdot\|_{F}$ denote the Frobenius norm (or Hilbert Schmidt norm on the finite dimensional $M_n(\mathbb{C})$). I am looking for estimates of the ...

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 ...

In my studies of applied analysis and applied linear algebra, this interesting problem and concept came up: Let us consider the space of all $ m \times n $ real matrices, and define a scalar ...

Suppose $C$ is a $n$ by $n$ real symmetric matrix, and $x\in R^n$. Is there an operator norm of $C$ for $\max\frac{\Vert x \Vert _1}{\sqrt {x'Cx}}$? If I decompose $C$ into $A'A = C^{-1}$, It seems ...

I know that for two symmetric positive semi-definite (non-diagonal) matrices $A,B$, the inequality asserts that the following does not hold for all $p > 1$ $$A \succeq B \succeq 0 \Rightarrow A^p \...

I'm working on a problem and was lead to trying to find an approximation for the square root of a matrix. I came across a way of doing this using holomorphic functional calculus. However, my first ...