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Common solutions to a pair of linear matrix equations A1XB1 = C1 and A2XB2 = C2

Published online by Cambridge University Press:  24 October 2008

Sujit Kumar Mitra
Sujit Kumar Mitra
Affiliation:
Indiana University, Bloomington
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 213 - 216
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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