Common solutions to a pair of linear matrix equations A1XB1 = C1 and A2XB2 = C2
- 1 September 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 74 (2) , 213-216
- https://doi.org/10.1017/s030500410004799x
Abstract
Penrose (4) gave a necessary and sufficient condition for the consistency of the linear matrix equation AXB = C and also its complete class of solutions. A necessary and sufficient condition for the equations AX = C, XB = D to have a common solution was given by Cecioni (3) and an expression for the general common solution by Rao and Mitra ((6), p. 25). In the present paper, we obtain a necessary and sufficient condition for the equations A1XB1 = C1 and A2XB2 = C2 to have a common solution and also an expression for the general common solution. This result isuseful in computing a constrained inverse of a matrix, a concept originallyintroduced by Bott and Duffin(2) and recently extended by Rao and Mitra(7) who consider more general constraints with the object of bringing together the various generalized inverses and pseudoinverses under a common classification scheme.Keywords
This publication has 5 references indexed in Scilit:
- Theory and Application of Constrained Inverse of MatricesSIAM Journal on Applied Mathematics, 1973
- Series and parallel addition of matricesJournal of Mathematical Analysis and Applications, 1969
- A generalized inverse for matricesMathematical Proceedings of the Cambridge Philosophical Society, 1955
- On the algebra of networksTransactions of the American Mathematical Society, 1953
- On the Algebra of NetworksTransactions of the American Mathematical Society, 1953