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6
votes
0answers
167 views

Product $PVPVP$ is elementwise nonnegative?

Let $P\in \mathbb{R}^{n\times n}$ be the inverse of a positive definite M-matrix and $V\in \mathbb{R}^{n\times n}$ be any diagonal matrix. Prove (or disprove) that $PVPVP$ is elementwise nonnegative. ...
3
votes
0answers
210 views

An optimization problem over real symmetric matrices

Given an $n\times s$ matrix $P$ of positive real numbers and $T\geq n$, find (either by a formula or an algorithm) the real symmetric $n\times n$ Z-matrix $A$ which maximizes $\min\limits_{1\leq ...
1
vote
0answers
109 views

Bounding the Schur's complement of similiar matrices

Assume the following: • $L\leq K$ . • $\Gamma\in M_{K,L}$ is a $L$ rank ${ 0,1} $ matrix, without identical rows or the zeros row. • $N\in M_{K,K}$ is a diagonal matrix, whose diagonal is a ...
0
votes
0answers
157 views

When does a real-valued function of a matrix depend only on eigenvalues?

Let $\mathcal{N}$ be the space of all $n \times n$ matrices that are similar to some nonnegative matrix with zero diagonal and let $f: \mathcal{N} \to \mathbb{R}$ be a continuously differentiable ...