A comment on some recent results concerning the reverse order law for {1,3,4}-inverses

作者：Cvetkovic Ilic Dragana S^*; Pavlovic Vladimir

来源：Applied Mathematics and Computation, 2010, 217(1): 105-109.

DOI：10.1016/j.amc.2010.05.013

• Generalized inverse
• MP-inverse
• Reverse order law

This paper has been motivated by the one of Liu and Yang [D. Liu, H. Yang, The reverse order law for {1, 3, 4}-inverse of the product of two matrices, Appl. Math. Comp. 215 (12) (2010) 4293-4303] in which the authors consider separately the cases when (AB){1, 3, 4} subset of B{1, 3, 4}.A{1, 3, 4} and (AB){1, 3, 4} = B{1, 3, 4}.A{1, 3, 4}, where A is an element of C(nxm) and B is an element of C(mxn). Here we prove that (AB){1, 3, 4} subset of B{1, 3, 4}.A{1, 3, 4} is actually equivalent to (AB){1, 3, 4} = B{1, 3, 4}.A{1, 3, 4}. We show that (AB){1, 3, 4} subset of B{1, 3, 4}.A{1, 3, 4} can only be possible if n <= m and in this case, we present purely algebraic necessary and sufficient conditions for this inclusion to hold. Also we give some new characterizations of B{1, 3, 4}.A{1, 3, 4}.A{1, 3, 4} subset of (AB){1, 3, 4}.

• 出版日期2010-9-1