Generalized even and odd totally positive matrices

TL;DR

This paper introduces a generalized framework for oscillatory matrices based on cone theory, proving eigenvalue properties and spectral criteria for these matrices, including new classes called even and odd oscillatory matrices.

Contribution

It extends the concept of oscillatory matrices using cone theory and defines new classes of even and odd oscillatory matrices with spectral analysis.

Findings

Eigenvalues of generalized oscillatory matrices are positive and simple.

Spectral properties and criteria for generalized even and odd oscillation are established.

Examples illustrate the new classes of matrices.

Abstract

A generalization of the definition of an oscillatory matrix based on the theory of cones is given in this paper. The positivity and simplicity of all the eigenvalues of a generalized oscillatory matrix are proved. The classes of generalized even and odd oscillatory matrices are introduced. Spectral properties of the obtained matrices are studied. Criteria of generalized even and odd oscillation are given. Examples of generalized even and odd oscillatory matrices are presented.