Cogredient Standard Forms of Orthogonal Matrices over Finite Local Rings of Odd Characteristic

TL;DR

This paper introduces a canonical form for orthogonal matrices over finite local rings of odd characteristic, aiding in classification and analysis of such matrices in algebraic structures.

Contribution

It provides a cogredient standard form for orthogonal spaces over finite local rings of odd characteristic, a novel classification tool in this context.

Findings

Established a cogredient standard form for orthogonal matrices

Facilitated classification of orthogonal spaces over finite local rings

Enhanced understanding of algebraic structures in finite rings

Abstract

In this work, we present a cogredient standard form of an orthogonal space over a finite local ring of odd characteristic.