J4 ›› 2011, Vol. 46 ›› Issue (4): 78-81.

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The reverse order law for {1,2,3}-inverse and {1,2,4}-inverse of products of two matrices

ZHANG Feng-xia1,  LI Ying1,2, ZHAO Jian-li1   

  1. 1. School of Mathematics Science, Liaocheng University,  Liaocheng 252059, Shandong, China;
    2. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2010-03-12 Published:2011-04-21


The reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of product of two matrices have been studied by applying the product singular value decomposition P-SVD and the characters of generalized inverse. The necessary and sufficient conditions of (AB){1,2,3}⊆B{1,2,3}A{1,2,3} and (AB){1,2,4}⊆B{1,2,4}A{1,2,4}are obtained. Then equivalent conditions of (AB){1,2,3}=B{1,2,3}A{1,2,3}  and (AB){1,2,4}=B{1,2,4}A{1,2,4} are obtained.

Key words: reverse order law; Generalized inverse; P-SVD

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