The Metapositive Definite  Self-Conjugate  Solution  of the Matrix Equation AXB=C over a Skew Field

数学季刊 ›› 1995, Vol. 10 ›› Issue (3): 42-51.

The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field

Department of Math.,Changwei Teachers College,Weifang,261043

收稿日期:1994-11-18 出版日期:1995-09-30 发布日期:2025-03-12

The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field

Department of Math.,Changwei Teachers College,Weifang,261043

Received:1994-11-18 Online:1995-09-30 Published:2025-03-12

摘要/Abstract

摘要： Let F be the strong p-division ring [4].This paper is sequel to [1].Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented.Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.

关键词: the strong p-division ring, matrix equation, metapositive definite self-conjugate matrix

Abstract: Let F be the strong p-division ring [4].This paper is sequel to [1].Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented.Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.

Key words: the strong p-division ring, matrix equation, metapositive definite self-conjugate matrix

中图分类号:

O153

王卿文. The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field[J]. 数学季刊, 1995, 10(3): 42-51.

Wang Qingwen. The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field[J]. Chinese Quarterly Journal of Mathematics, 1995, 10(3): 42-51.

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The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field

The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field

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