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Let $A\in\mathcal M_n$ be an $n\times n$ real [symmetric] matrix which depends smoothly on a [finite] set of parameters, $A=A(\xi_1,\ldots,\xi_k)$. We can view it as a smooth function $A:\mathbb R^k\...

This question is related to another question, but it is definitely not the same. Is it always possible to diagonalize (at least locally around each point) a family of symmetric real matrices $A(t)$ ...

Consider the $N \times N$ matrix $$A_{\alpha}=\begin{pmatrix} \lambda_1 & -1 & -\alpha & 0 & \cdots & 0\\ -1 & \lambda_2 & -1 & -\alpha & \cdots & 0\\ -\alpha &...

Let $A$ be a $n\times n$ matrix. Let $\|A\|$ be the spectral norm of $A$, and $\rho(A)$ be the spectral radius. I am wondering whether the following statement is true. There exists universal ...

Hi, everyone! Is there any efficient way to simplify the following tensor product $X \otimes X + X^T \otimes X^T$, where $X$ is a square $n \times n$ matrix. My goal is to efficiently compute the ...

I'm currently interested in how discontinuous can get the eigenprojections of a continuous function taking values in a particular subspace of symmetric matrices. I've been searching everywhere for an ...