Computation of the canonical form for the matrices of chains and cycles of linear mappings

TL;DR

This paper extends Van Dooren's stable algorithm for computing Kronecker's canonical form of matrix pencils to the matrices of cycles of linear mappings, enabling more comprehensive analysis of such structures.

Contribution

The paper introduces an extension of Van Dooren's algorithm to handle matrices of cycles of linear mappings, broadening its applicability.

Findings

Algorithm is numerically stable using only unitary transformations

Successfully computes irregular summands in cycles of linear mappings

Enhances understanding of canonical forms for complex matrix structures

Abstract

Paul Van Dooren [Linear Algebra Appl. 27 (1979) 103-140] constructed an algorithm for the computation of all irregular summands in Kronecker's canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary transformations. We extend Paul Van Dooren's algorithm to the matrices of a cycle of linear mappings.