矩阵方程X^s+A~*X^(-t)A=I_n的Hermite正定解的特征值分布

On the Distribution of the Eigenvalues of the Hermite Positive Definite Solutions of Matrix Equation X^s+A~*X^(-t)A=I_n

给出了矩阵方程X^s+A~*X^-t A=I_n在||A||-2≤(s/s+t)(t/s+t)^(t/s)时Hermite 正定解的最小、最大特征值的所在区间,并且讨论了其余特征值的分布情况.

In this paper, the eigenvalues of the Hermite positive definite solutions of the matrix t equation X^s+A~*X^-t A=I_n在||A||-2≤(s/s+t)(t/s+t)^(t/s) are given and studied and the intervals of minimum and maximal eigenvalues of the solutions are presented. The distribution of other eigenvalues is also discussed.