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gh合同
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  gh-congruence
     The GH-congruence Canonical Forms of Two Classes of Matrix Couples over a Quaternion Field
     两类四元数矩阵偶的GH合同标准形
短句来源
     GH-congruence Canonical Form of Quaternion Matrix and Simultaneous Diagonalization of Matrices
     四元数方阵的GH合同标准形与同时对角化
短句来源
     3°A determinant of a self-conjugate matrix is not changed in value under the GH-congruence trasformations;
     3°自共矩矩阵的行列式在GH合同变换下不变值;
短句来源
     In this paper,first the GH-congruence canonical forms of positive semidefinite and definite quaternion matrices are given,meanwhile a sufficient and necessary condition of GH-congruence for two positive semidifinite(difinite) quaternion matrices do also.
     给出半正定与正定四元数阵的GH合同标准形,以及两半正定(正定)四元数阵GH合同的充要条件.
短句来源
     Then simultaneous GH-congruence reduced forms for two self-conjugate matrices and some results about the simultaneous GH-congruence diagonalization of quaternion matrices.
     并给出两自共轭四元数阵(其一为半正定)的同时GH合同简化形,由此得到两自共轭同时对角化问题的一些结果.
短句来源
  gh congruence
     In this paper, the GH congruence canonical forms for matrix couples  and  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.
     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 .
短句来源
     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.
     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
短句来源
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In this paper the following theorerms and propositions are proved:1°For any self-conjugate matrix A of rank γ over the skew-field of quaternions there exists a left tall matrix L such that L'AL is a γ-rowed non-singular self-conjugate matrix;2°Unique decomposition theorem of positive definite matrix;3°A determinant of a self-conjugate matrix is not changed in value under the GH-congruence trasformations;4°Some equivalent propositions about positive definite matrices and semi-positive definite matrices.

本文证明了下面一些定理与命题: 1°对四元数体上任意秩数为r的自共轭矩阵A恒存在一个左高矩阵L使得为一个r阶的非奇异自共轭矩阵; 2°正定矩阵的唯一分解定理; 3°自共矩矩阵的行列式在GH合同变换下不变值; 4°关于正定矩阵与半正定矩阵的一些等价命题。

In this paper, the GH congruence canonical forms for matrix couples  and  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.

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

In this paper,first the GH-congruence canonical forms of positive semidefinite and definite quaternion matrices are given,meanwhile a sufficient and necessary condition of GH-congruence for two positive semidifinite(difinite) quaternion matrices do also.Then simultaneous GH-congruence reduced forms for two self-conjugate matrices and some results about the simultaneous GH-congruence diagonalization of quaternion matrices.

给出半正定与正定四元数阵的GH合同标准形,以及两半正定(正定)四元数阵GH合同的充要条件.并给出两自共轭四元数阵(其一为半正定)的同时GH合同简化形,由此得到两自共轭同时对角化问题的一些结果.

 
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