In:
Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-7
Abstract:
The matrix equation A X B H = E with S X = X R or P X = s X Q constraint is considered, where S, R are Hermitian idempotent, P, Q are Hermitian involutory, and s = ± 1 . By the eigenvalue decompositions of S, R , the equation A X B H = E with S X = X R constraint is equivalently transformed to an unconstrained problem whose coefficient matrices contain the corresponding eigenvectors, with which the constrained solutions are constructed. The involved eigenvectors are released by Moore-Penrose generalized inverses, and the eigenvector-free formulas of the general solutions are presented. By choosing suitable matrices S, R , we also present the eigenvector-free formulas of the general solutions to the matrix equation A X B H = E with P X = s X Q constraint.
Type of Medium:
Online Resource
ISSN:
1110-757X
,
1687-0042
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2013
detail.hit.zdb_id:
2578385-3
SSG:
17,1
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