Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix

In this note, we give a complete characterization of square matrices of size $n$ over a commutative field which can be expressed as a product of a nilpotent matrix and an involutive matrix and matrices which can be expressed as a product of a nilpotent matrix and an idempotent matrix, in terms of invariant factors.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-18
DOI
https://doi.org/10.5281/zenodo.21992659
Primary Topic
Matrix Theory and Algorithms
Type
preprint
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preprint

Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix

Flavien Mabilat
Zenodo (CERN European Organization for Nuclear Research)
Matrix Theory and Algorithms
preprint

Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix

Flavien Mabilat
preprint en

Abstract

In this note, we give a complete characterization of square matrices of size $n$ over a commutative field which can be expressed as a product of a nilpotent matrix and an involutive matrix and matrices which can be expressed as a product of a nilpotent matrix and an idempotent matrix, in terms of invariant factors.

Zenodo (CERN European Organization for Nuclear Research)
Matrix Theory and Algorithms
DOIOpen Access PDFOpenAlex
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Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix — Flavien Mabilat · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS