Positivity criteria generalizing the leading principal minors criterion

TL;DR

This paper introduces generalized positivity criteria for Hermitian matrices, replacing leading principal minors with sums of minors, thus broadening the tools for inertia analysis.

Contribution

It presents a novel generalization of the leading principal minors criterion using sums of minors for Hermitian matrices.

Findings

New positivity criteria using sums of minors

Broader applicability in inertia problems

Potential simplifications in matrix analysis

Abstract

For each Hermitian matrix, we prove that instead of the leading principal minors some of their sums can be used in the leading principal minors criterion and in other inertia problems.