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5
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0answers
129 views

An inequality concerning non-negative integer matrices with constant row and column sums

[I posted this question on math.stackexchange a few weeks back, but no luck there so far: ...
3
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0answers
264 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 ...
2
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0answers
69 views

Polynomials with positive coefficients passing through fixed points/range of Vandermonde matrices

I'll give two equivalent statements of the setup, then give my questions. Fix integers $M \leq N$ and define the Vandermonde-like matrix $V_{M,N}[i,j] = (1 - \frac{i}{M})^{j-1}$ for $i \in ...
1
vote
0answers
216 views

A Perron-Frobenius problem

Let $A$ be an irreducible nonnegative matrix with column sums equal to 1. Let $b\in R^n$ have components summing to 0, and let $u$ be the solution of $u=Au+b$ with components summing to 1 (unique ...
1
vote
0answers
87 views

Likelihood convexification

I am doing constrained vector optimization using a non-convex non-linear likelihood function. My problem is of the following form: $$\begin{align*}\hat Q &= \underset{\vec Q}{\arg\min} -\log ...
1
vote
0answers
97 views

Spectrum of primitive nonnegative integer matrices

Let $P(X) = a_nX^n + \cdots + a_1X + a_0$ with $a_i \in \mathbb Z$. Question 1. Is there an efficient criterion on the $a_i$ to decide if there exists a primitive nonnegative integer matrix with ...
1
vote
0answers
118 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
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0answers
169 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 ...