【摘要】 该文给出两类四元数矩阵偶〈 A,B1〉与〈 A,B2 〉的 GH合同标准形 ,其中 A为半正定自共轭阵 ,B1为斜自共轭阵 ,B2 为自共轭阵 .由此分别得到 (广义 )半正定与正定四元数矩阵的 GH合同标准形 ,以及矩阵同时对角化问题的若干个结果更多还原

【Abstract】 In this paper, the GH congruence canonical forms for matrix couples <A,B 1> and <A,B 2> over a quaternion field are given, where A is a positive semidefinite self conjugate matrix, B 1 a skew self conjugate matrix and B 2 a self conjugate matrix. Moreover, it is obtained that the GH congruence canonical forms for (generalized) positive semidefinite and definite matrices and some results about the simultaneous GH congruence diagonalization of quaternion matrices.更多还原