华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (3): 16-21.

• 数学 统计学 • 上一篇    下一篇

任意体上矩阵广义逆的反序律

刘永辉1，2， 巩子坤2， 魏木生1   

  1. 1. 华东师范大学 数学系，上海 200062; 2. 枣庄学院 数学系，枣庄 277160
  • 收稿日期:2002-12-06 修回日期:2003-04-25 出版日期:2004-09-25 发布日期:2004-09-25
  • 通讯作者: 刘永辉

Reverse Order Laws for Generalized Inverses of Matrices on An Arbitrary Skew Field

LIU Yong-hui1,2, GONG Zi-kun2, WEI Mu-sheng1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. Department of Mathematics, Zaozhuang College, Zaozhuang 277160, China
  • Received:2002-12-06 Revised:2003-04-25 Online:2004-09-25 Published:2004-09-25
  • Contact: LIU Yong-hui

摘要： 证明了任意体上矩阵乘积的一条分解定理. 利用该分解定理作为工具，获得了任意体上矩阵乘积的g-逆和自反g-逆的反序律的充分必要条件.

关键词: 体, 矩阵分解, g-逆, 自反g-逆, 反序律, 体, 矩阵分解, g-逆, 自反g-逆, 反序律

Abstract: In this paper, we prove a decomposition theorem of matrix pair over an arbitrary skew field. By applying the decomposition theorem, we obtain some neccessary and sufficient conditions of reverse order laws for g-inverse and reflexive g-inverse of matrix products on an arbitrary skew field.

Key words: matrix decomposition, g-inverse, reflexive g-inverse, reverse order law, Skew field, matrix decomposition, g-inverse, reflexive g-inverse, reverse order law

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