Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

TL;DR

This paper provides canonical tridiagonal forms for various matrix classes under congruence and *congruence over algebraically closed fields, aiding classification and analysis of these matrix types.

Contribution

It introduces explicit tridiagonal canonical forms for matrices and matrix pairs under congruence and *congruence, extending classification results to multiple matrix classes.

Findings

Canonical tridiagonal forms for matrices under congruence and *congruence.

Canonical forms for pairs of symmetric, skew-symmetric, and Hermitian matrices.

Results applicable over algebraically closed fields with characteristic not 2.

Abstract

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2.