方阵分解为幂零矩阵与对合矩阵或幂等矩阵的乘积
Decomposition of a square matrix into a product of a nilpotent matrix and an involutive or idempotent matrix
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中文总结 AI 辅助
本研究以不变因子为依据，完整刻画了交换域上n阶方阵可分解为幂零矩阵与对合矩阵或幂等矩阵乘积的条件。
中文摘要 AI 辅助
在本注记中，我们以不变因子为依据，完整刻画了交换域上n阶方阵中可表示为幂零矩阵与对合矩阵乘积的矩阵，以及可表示为幂零矩阵与幂等矩阵乘积的矩阵。
英文摘要
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.
