Littlewood's algorithm and quaternion matrices

TL;DR

This paper extends Littlewood's algorithm to quaternion matrices with real spectrum, providing a canonical form under unitary similarity, and strengthens Schur's triangularization theorem for such matrices.

Contribution

It introduces a new extension of Littlewood's algorithm for quaternion matrices with eigenvalues of geometric multiplicity one, enhancing matrix reduction techniques.

Findings

Extended Littlewood's algorithm to quaternion matrices.

Provided a strengthened Schur's triangularization theorem for quaternion matrices.

Achieved canonical forms under unitary similarity for specific quaternion matrices.

Abstract

A strengthened form of Schur's triangularization theorem is given for quaternion matrices with real spectrum (for complex matrices it was given by Littlewood). Littlewood's algorithm for reducing a complex matrix to a canonical form under unitary similarity is extended to quaternion matrices whose eigenvalues have geometric multiplicity 1.