Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (1): 36-41.

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New Definitions of Partial Ordering of Generalized Inverse(Chinese)

HUANG Xuan-chen, WEI Mu-sheng   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, t China
  • Received:2005-09-12 Revised:2006-03-02 Online:2007-01-25 Published:2007-01-25
  • Contact: WEI Mu-sheng

Abstract: By using the concept of partial ordering of matrix, some new definitions of partial ordering were put forward, such as $\boldsymbol{A}\leqslant^{\{1\}}\boldsymbol{B}\Leftrightarrow \boldsymbol{A}\boldsymbol{A}\{1\}=\boldsymbol{B}\boldsymbol{A}\{1\},\boldsymbol{A}\{1\}\boldsymbol{A}=\boldsymbol{A}\{1\}\boldsymbol{B} $ and $\boldsymbol{A}\leqslant^{\{1,2\}}\boldsymbol{B}\Leftrightarrow \boldsymbol{A}\boldsymbol{A}\{1,2\}=\boldsymbol{B}\boldsymbol{A}\{1,2\},\boldsymbol{A}\{1,2\}\boldsymbol{A}=\boldsymbol{A}\{1,2\}\boldsymbol{B}$. Four situations were discussed in detail, according to which, sufficient and necessary conditions of the new partial ordering have been derived.

Key words: generalized inverse, partial ordering, matrix, generalized inverse, partial ordering

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