关于二次Hermite矩阵方程的解的注记

Note on the Solutions of the Quadratic Hermite Matrix Equation

给出二次Hermite矩阵方程X*AX=A的解的关系,讨论更一般的二次Hermite矩阵方程X*AX=B有解的条件和通解的表达,并在限定条件下对二次矩阵方程的一个公开问题作了解答.

Gives the relationship among the solutions of the quadratic Hermite matrix equation of X＊AX=A,and obtains a condition of solutions of a matrix equation of X＊AX=B and the general forms of its solutions. Finally, discusses an open problem of quadratic matrix equation under some conditions.