All Questions

Endow $\mathbb{C}^{d \times d}$ with the norm induced by the Euclidean norm on $\mathbb{C}^d$. It is well-known (to those who know it well, I guess) that the spectrum $\sigma(A)$ of a matrix $A \in \...

Disclaimer. This is a cross-post from math.SE where I asked a variant of this question two days ago which has been positively received but not has not received any answers. Let $A$ be a complex ...

Let $A$ and $B$ be two matrices of eigenvalues $\lambda_i$ and $\mu_i$, respectively. The spectral variation of $B$ w.r.t. $A$ and the eigenvalue variation of $B$ and $A$ are, respectively, \begin{...

Let $G$ be an undirected, simple, bipartite graph with parts $V$ (having $n$ vertices) and $W$ (having $m$ vertices). Define the following $n$-by-$n$ matrix: for any $i,j \in V$, $$a_{ij} = |N_i \cap ...

I am working with a class of matrices $A$ which are non-negative-definite, not symmetric, and have maximum eigenvalue less than 1. I am interested in the spectral properties of the matrix $H = A(I - ...