All Questions

$\newcommand\norm[1]{\lVert#1\rVert} \newcommand\opnorm[1]{\norm{#1}_{\text{op}}} \newcommand\Frnorm[1]{\norm{#1}_{\text F}}$Define \begin{align*} S_t=\{ (A,B)\in\mathbb{R}^{n\times n}\times\...

Let $U$ be an $n\times n$ orthogonal matrix, i.e. $U\in\mathbb{R}^{n \times n}$. For any non-empty ordered sets $S_1,S_2\subset\{1,2,...,n\}$, define $U_{S_1S_2}$ to be an $|S_1|\times|S_2|$ submatrix ...

ORIGINAL QUESTION Let $\lambda_{1}\left(\cdot\right)$ be the larger eigenvalue of a $2\times2$ matrix and $\lambda_{2}\left(\cdot\right)$ the smaller eigenvalue of a $2\times2$ matrix. Is it true ...