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On Linear Matrix Equations

Published online by Cambridge University Press:  20 November 2018

P. Scobey
Affiliation:
Department of Mathematics St. Mary's University, Halifax, N.S., B3H 3C3
D.G. Kabe
Affiliation:
Department of Mathematics St. Mary's University, Halifax, N.S., B3H 3C3
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Abstract

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Some results from the theory of minimization of vector quadratic forms (subjected to linear restrictions) are used to obtain particular solutions to the usual types of linear matrix equations. An answer to a question raised by Greville [1] is supplied.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Greville, T. N. E., Solution of the matrix equation XAX = X and relations between oblique and orthogonal projectors, SIAM J. Appl. Math., 26 (1974), 828-834.Google Scholar
2. Kabe, D. G., Minima of vector quadratic forms with applications to statistics, Metrika 12 (1968), 155-160.Google Scholar
3. Khatri, C. G. and Mitra, S. K., Hermitian and nonnegative definite solutions of linear matrix equations, SIAM J. Appl. Math., 31 (1976), 579-585.Google Scholar
4. Mitra, S. K., Fixed rank solutions to linear matrix equations, Sankhya Ser. A, 35 (1972), 387-392.Google Scholar
5. Mitra, S. K., Common solutions to a pair of matrix equations, A1XB1 = Cx, A2XB2= C2, Proc. Cambridge Phil. Soc, 74, (1973), 213-216.Google Scholar
6. Mitra, S. K., The matrix equation AXB + CXD = E, SIAM J. Appl. Math. 32 (1977), 823-825.Google Scholar
7. Rao, C. R., Estimation of variance and covariance components in linear models, J. Amer, Statisti. Assoc., 67 (1972), 112-115.Google Scholar