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Reverse Order Laws for the con-s-k-EP Weighted Generalized Inverses

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Author Affiliations

  • 1Ramanujan Research Centre, Department of Mathematics, Govt. Arts College (Autonomous), Kumbakonam, Tamilnadu, INDIA
  • 2Ramanujan Research Centre, Department of Mathematics, Govt. Arts College (Autonomous), Kumbakonam, Tamilnadu, INDIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (8), Pages 1-7, September,12 (2013)

Abstract

If A is a con s-k-EP matrix, then the reverse order laws for the con-s-k-EP weighted generalized inverse of A ( with respect to the given matrices M,N) is a matrix which satisfies AAA = A, AAA = A and that MAA and that AAN are symmetric under certain conditions on M,N. It is shown that the weighted generalized inverse exists if and only if A N A MA = A, in which case the inverse is NAM. When M.N are identity matrices, this reduces to the well known result that the weighted generalized inverse of a con-s-k-EP matrix when it exists, must be A.

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