Linear complementarity on simplicial cones and the congruence orbit of matrices

TL;DR

This paper explores the relationship between the congruence orbit of matrices and the linear complementarity problem on simplicial cones, providing a classification framework connecting matrix orbits and complementarity theory.

Contribution

It establishes an equivalent classification of matrices based on their congruence orbit and the associated simplicial cones within complementarity theory.

Findings

Classification of matrices via congruence orbits and simplicial cones

Connection between matrix orbits and complementarity problems

Unified framework for matrix analysis in complementarity theory

Abstract

The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones -- we give equivalent classification of matrices from the point of view of the complementarity theory.