On the ``Reverse Order Law'' Related to the Generalized Inverse of Matrix Products
- 1 July 1966
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 13 (3) , 439-443
- https://doi.org/10.1145/321341.321353
Abstract
The “reverse order law” related to ordinary inverses of matrix products, i.e., ( AB ) -1 = B -1 A -1 , is generally not transferable to the generalized inverse. There are, however, applications in which the reverse order law related to the generalized inverse reveals interesting properties in certain classes of matrices. In this paper, some necessary and sufficient conditions for the reverse order property to hold are given.Keywords
This publication has 9 references indexed in Scilit:
- Representations for the Generalized Inverse of Sums of MatricesJournal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1965
- An iterative method for computing the generalized inverse of an arbitrary matrixMathematics of Computation, 1965
- Generalized Inverse Computations Using the Gradient Projection MethodJournal of the ACM, 1964
- The Matrix Pseudoinverse and Minimal Variance EstimatesSIAM Review, 1964
- Note on the Generalized Inverse of the Product of MatricesSIAM Review, 1964
- The Computation of the Generalized Inverse of singular or Rectangular MatricesThe American Mathematical Monthly, 1963
- Some Applications of the Pseudoinverse of a MatrixSIAM Review, 1960
- The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear EquationsSIAM Review, 1959
- A generalized inverse for matricesMathematical Proceedings of the Cambridge Philosophical Society, 1955