I stumbled on the following simple matrix norm, which I haven't seen elsewhere. I wonder if it is well known, has a name, and has been studied elsewhere. The definition of this nor …

I have the following, probably very elementary question: Let $Cl^{p,q}$ be the Clifford algebra on generators $e_i$, $i=1, \ldots, p+q$ with $e_i e_j = -e_j e_i$ and $e_{i}^{2}=-1$ …

Hi all, Suppose that $\mathbf{f}=[f_1, f_2,\ldots,f_m]$ and $\mathbf{g}=[g_1,g_2,\ldots,g_m]$ are two $m$-dimensional vectors. All $f_i$'s are chosen uniformly randomly from a fin …

Inspired by this question, I would like to determine the probability that a random knot of 6 unit sticks is a trefoil. This naturally leads to the following question: Is there a …

Dear all, I stumbled on this question due to an application in physics, but I find it hard to find useful references for it. I looked into literature on projective geometry and po …

Let $M$ be a smooth Riemannian manifold, let $R$ be the Riemannian curvature operator, and let $p$ be a point in the manifold. With respect to any orthonormal basis of the tangent …

Consider a real square matrix $A$ of size $n\times n$. Under which conditions on $A$ does there exist a row-stochastic matrix $U$ (non-negative, rowsums = 1), such that $A'=U^{-1}A …

Hello all, This is a question that might or might not be related to my previous one. Imagine you have two matrices: Matrix $\mathbf{\Phi}=[\Phi_1,\ldots,\Phi_M]\in\mathbb{R}^{L …

Hi, I have a matrix of the form $A=VDV^H$, where $V$ is a $M \times 2M$ complex matrix, $D$ is a $2M \times 2M$ diagonal real matrix, thus the dimension of $A$ is $M \times M$. …

Hi, let $L$ be a lattice isomorphic to $\mathbb{Z}^r$ for some positive integer $r$ and $E=L\otimes \mathbb{R}$. An integral paving in $E$ is a set $\Sigma$ of integral polytopes …

I'm trying to understand the standard $GL(3,\mathbb{R})$ action on the 15-dimensional space of possible values for the derivative of the Riemann curvature tensor of a 3-dimensional …

I am multiplying a matrix $A$ with vector $p$. However, the matrix $A$ isn't accurate. Some (a very small fraction) of the element's value is changed from $a_{i,j}$ to {0,$-a_{i, …

Let $\mathbf{A}_1$ and $\mathbf{A}_2$ be two $N\times N$ hermitian matrices. Their Joint Numerical Range is defined as the 2-D set \begin{align} \mathbb{S}_2=\{[\textbf{u}^H\mathbf …

I encountered an inequality when reading a paper. Can someone help to show how to prove it? Let be the spectral radius of matrix $A$ or $\rho(A)=\max{|\lambda|, \lambda \text{ are …

Let $R = \mathbb{Z}[x_{1}, \dots, x_{r}]$. Let $X$ be $n \times n$ matrix with entries in $R$. Let $Y$ be $m \times m$ matrix with entries in $R$ formed from $\mathbb{Z}$-linear or …