Algebraic analysis characterizes square matrix factorizations over commutative fields using invariant factors, establishing exact decomposition criteria.
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) studied this question.
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