Journal
APPLIED MATHEMATICS LETTERS
Volume 22, Issue 12, Pages 1786-1788Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2009.06.020
Keywords
Matrix equation; Eigenvalue; Positive definite matrix; Symmetric matrix
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The following matrix equations: A(T)XB + B(T)X(T)A = C and A(T)XB + B(T)XA = C, are encountered in many systems and control applications, and these matrix equations contain several linear matrix equations as special cases. In the present work, we introduce the inequalities for the determinant of the solutions of these matrix equations, separately. Then using these inequalities, we introduce a lower bound for the product of eigenvalues of the solutions to the matrix equations. (C) 2009 Elsevier Ltd. All rights reserved.
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