实对称方阵的同时合同简化型与对角化

Simultaneous congruence reduced forms and diagonalization of real symmetric matrices

给出一半正定对称阵Ａ与一对称阵Ｂ 的同时合同简化型，并给出较之两半正定对称阵更弱的条件，证明了两矩阵可同时合同对角化，从而在实数域上改进了已有文献的相应结果．

The simultaneous congruence reduced forms of a positive semidefinite symmetric matrix A and a symmetric matrix B is given.Moreover a weeker condition for simultaneous congruence diagonalization of two symmetric matrices is obtained,and the corresponding results of matrices over real number field are improved.