A regularization algorithm for matrices of bilinear and sesquilinear forms

TL;DR

This paper introduces a unitary transformation-based algorithm that decomposes square complex matrices into a direct sum of a nonsingular matrix and singular Jordan blocks, aiding matrix classification.

Contribution

The paper presents a novel regularization algorithm for matrices of bilinear and sesquilinear forms using only unitary transformations.

Findings

Efficient matrix decomposition into canonical forms

Applicable to complex matrices of bilinear and sesquilinear forms

Provides a constructive method for matrix regularization

Abstract

We give an algorithm that uses only unitary transformations and for each square complex matrix constructs a *congruent matrix that is a direct sum of a nonsingular matrix and singular Jordan blocks.