Mock Tridiagonal Systems

TL;DR

This paper introduces mock tridiagonal systems, a generalized concept that relaxes irreducibility, and demonstrates their use in constructing specific tridiagonal systems, advancing the classification of such systems.

Contribution

It defines mock tridiagonal systems and shows how they can be used to construct and classify tridiagonal systems with particular properties.

Findings

Mock tridiagonal systems generalize traditional systems.

They enable construction of tridiagonal systems with specified features.

Progress towards classifying tridiagonal systems up to isomorphism.

Abstract

We introduce the notion of a {\it mock tridiagonal system}. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain non-vanishing condition. We show how mock tridiagonal systems can be used to construct tridiagonal systems that meet certain specifications. This paper is part of our ongoing project to classify the tridiagonal systems up to isomorphism.