J4 ›› 2010, Vol. 45 ›› Issue (10): 9-14.

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The weighted Moore-Penrose inverse over integral domains

WANG Hong-xing1,2, LIU Xiao-ji3   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241;
    2. Department of Mathematics, Huainan Normal University, Huainan 232001, Anhui, China;
    3. College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China
  • Received:2009-12-22 Online:2010-10-16 Published:2010-10-19

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Abstract:

The generalized Moore-Penrose inverse is investigated over integral domains. New determinantal representations of the weighted Moore-Penrose inverse are introduced, and necessary and sufficient conditions for its existence over an integral domain are obtained.

Key words: integral domain; subdeterminants; weighted Moore-Penrose inverse

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