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

Flavien Mabilat

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arXiv · 2608.17569

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

Flavien Mabilat

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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.

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Flavien Mabilat. 2026-08-18. Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix. https://arxiv.org/abs/2608.17569

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