The Strong Singular Value Property for Matrices

TL;DR

This paper introduces the strong singular value property, a new concept to analyze which lists of nonnegative real numbers can be singular values of matrices with specific zero-nonzero patterns.

Contribution

The paper develops the strong singular value property and applies it to characterize possible singular value lists for matrices with prescribed zero-nonzero patterns.

Findings

Introduces the strong singular value property.

Provides criteria for singular value realizability with pattern constraints.

Advances understanding of matrix spectral properties with zero patterns.

Abstract

A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.