A complete unitary similarity invariant for unicellular matrices

TL;DR

This paper provides a comprehensive set of conditions to determine when a complex matrix is unitarily similar to a fixed indecomposable (unicellular) matrix, advancing the classification of such matrices.

Contribution

It introduces necessary and sufficient criteria for unitary similarity to a given unicellular matrix, offering a complete invariant for this class.

Findings

Established a complete unitary similarity invariant for unicellular matrices

Derived necessary and sufficient conditions for unitary similarity

Enhanced understanding of matrix similarity classification

Abstract

We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A