Degeneration order of $3\times 3$ nilpotent matrix tuples

TL;DR

This paper characterizes the degeneration order of $3\times 3$ nilpotent matrix tuples, showing it is governed by rank conditions, thus providing a clear criterion for their classification.

Contribution

It explicitly determines the degeneration order of $3\times 3$ nilpotent matrix tuples based on rank conditions, advancing understanding of their similarity classes.

Findings

Degeneration order is characterized by rank conditions.

The classification of nilpotent matrix tuples is explicitly described.

Provides a criterion for comparing similarity classes of matrix tuples.

Abstract

The degeneration order of simultaneous similarity classes of $3\times 3$ nilpotent matrix tuples is determined, and is shown to be given by rank conditions.