Computing Common Eigenvectors and Simultaneous Triangulation

TL;DR

This paper introduces an efficient algorithm to find common eigenvectors of multiple matrices, enabling the determination and computation of simultaneous triangulation, which is useful in various linear algebra applications.

Contribution

The paper presents a novel, efficient algorithm for computing common eigenvectors and determining simultaneous triangulation of matrices, advancing computational linear algebra methods.

Findings

Algorithm successfully computes common eigenvectors for multiple matrices.

Method determines whether matrices admit simultaneous triangulation.

Provides a basis for matrices that can be triangulated simultaneously.

Abstract

We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so, for computing a corresponding basis.