All Questions

Before asking the question I do need some notations. $G$ a (torsion-free) group, $\mathbb{Z}^{´}=\mathbb{Z}[\frac{1}{2}]$ $R:= \mathbb{Z}[G]$, $R^{´}=\mathbb{Z}^{´}[G]$ group rings. $Mat_{n}(R)$ the ...

One can show that the following statement holds: Given symmetric matrix $A \in \Re^{n \times n}$ and tall matrix $B \in \Re^{n \times p}$ with full column rank, $$\begin{bmatrix}A & B \\ B^T &...

This seems like a standard problem, but unable to find a solution online. Suppose we have two singular PSD matrices A and B with the following assumptions: $ 0 < x \leq ||A|| \leq y$ $ 0 < ||...

Let $T(n,k)$ be a $n \times n$ symmetric Toeplitz matrix, where all the entries of first $k$ super-diagonal (and sub-diagonal), last $k-1$ super-diagonal (and sub-diagonal) are ones, and rest of the ...

Given an $n\times n$ invertible matrix $\mathbf A$ and two column vectors $\mathbf u$, $\mathbf v\in\mathbb R^n$, suppose that $1 + {\mathbf v}^T {\mathbf A}^{-1}\mathbf u \neq 0$. Then the Sherman-...

The article Alesker, S. (2003). Quaternionic Monge-Ampere equations. The Journal of Geometric Analysis, 13(2), 205-238. has the following CLAIM: Claim. Let $A$ be an invertible hyperhermitian ...