关于矩阵方程X^s+A^TX^(-t)A=I_n的正定解

On Hermitian Positive Definite Solution of Matrix Equation

文章研究了矩阵方程Xs+ATX-tA=In 的正定解。给出了当矩阵A奇异时,正定解X的最大特征值为1;利用迭代方法讨论了A非奇异时。

In this paper,the hermitian positive definite solutions ofthe matrixequation X s +A T X -t A=I n are studied.The maxiˉmal eigenvalue of Xis given in case Ais singular.By means of iterative method,the existence and convergence of the solutions are showed in case Ais invertible.