泉州师范学院学报
泉州師範學院學報
천주사범학원학보
Journal of Quanzhou Normal College
2005年
6期
7~13
,共null页
半正定（正定）四元数阵 自共轭四元数阵 GH合同标准形 同时对角化
半正定（正定）四元數陣 自共軛四元數陣 GH閤同標準形 同時對角化
반정정（정정）사원수진 자공액사원수진 GH합동표준형 동시대각화
positive semidefinite （definite） quaternion matrix; self-conjugate quaternion matrix ; GH-congruence canonical form ; simultaneous diagonalization
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.
給齣半正定與正定四元數陣的GH閤同標準形,以及兩半正定(正定)四元數陣GH閤同的充要條件.併給齣兩自共軛四元數陣(其一為半正定)的同時GH閤同簡化形,由此得到兩自共軛同時對角化問題的一些結果.
급출반정정여정정사원수진적GH합동표준형,이급량반정정(정정)사원수진GH합동적충요조건.병급출량자공액사원수진(기일위반정정)적동시GH합동간화형,유차득도량자공액동시대각화문제적일사결과.
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.
