参数构成可对角化矩阵交换集的线性矩阵方程
Linear matrix equations with parameters forming a commuting set of diagonalizable matrices
AI总结：
本文证明参数为可对角化交换矩阵的线性矩阵方程的相容性、Drazin 逆构造解及标准方程相容三者等价，并给出解空间维数与典型方程应用。
摘要：
我们证明了以下命题彼此等价：参数构成可对角化矩阵交换集的线性矩阵方程相容；由 Drazin 逆构造的某个矩阵是该矩阵方程的解；所附带的标准线性矩阵方程相容。给定矩阵（相关矩阵）的零分量数量给出了解的仿射空间的维数。我们将这一理论结果应用于 Sylvester 方程、Stein 方程和 Lyapunov 方程。我们还给出了对可对角化矩阵交换序列的对角化矩阵集合的描述。
英文摘要：
We prove that the following statements are equivalent: a linear matrix equation with parameters forming a commuting set of diagonalizable matrices is consistent, a certain matrix constructed with the Drazin inverse is a solution of this matrix equation, the attached standard linear matrix equation is consistent. The number of zero components of a given matrix (the relevant matrix) gives us the dimension of the affine space of solutions. We apply this theoretical results to the Sylvester equation, the Stein equation, and the Lyapunov equation. We present a description of the set of the diagonalizing matrices for a commuting sequence of diagonalizable matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
