Canonical forms for a class of pairs of commuting nilpotent matrices under simultaneous similarity

2023/04/29 by Jiuzhao Hua, Hua, Jiuzhao · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #Cooperative Communication and Network Coding #FOS: Mathematics #General Mathematics (math.GM) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.00176

openalex publication_date 2023/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present canonical forms for all indecomposable pairs (A,B) of commuting nilpotent matrices over an arbitrary field under simultaneous similarity, where A is the direct sum of two Jordan blocks with distinct sizes. We also provide the transformation matrix X such that (A, X^-1BX) is in its canonical form.

Cited by

• Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

Related

• Canonical forms for pairs of commuting nilpotent 4× 4 matrices under simultaneous similarity
• Jordan forms for mutually annihilating nilpotent pairs
• The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
• Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size
• On triangular similarity of nilpotent triangular matrices