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《Journal of Jilin University (Science Edition)》 1980-02
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SELF-CONJUGATE MATRICES AND DETERMINANTS OF QUATERNIONS

Xie Bangjie(Department of Mathematics)  
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.
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