The Constrained Solutions of Two Matrix Equations |
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Authors: | An Ping Liao Zhong Zhi Bai |
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Affiliation: | (1) Department of Mathematics, Hunan University, Changsha 410082, P. R. China, Department of Mathematics and Information Sciences, Changsha University, Changsha 410003, P. R. China and Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China, CN;(2) State Key Laboratory of Scientific/Engineering Computing, Chinese Academy of Sciences, Institue of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100080, P. R. China E-mail: bzz@lsec.cc.ac.cn, CN |
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Abstract: | ![]() We study the symmetric positive semidefinite solution of the matrix equation AX 1 A T + BX 2 B T = C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation D T XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions. Received December 17, 1999, Revised January 10, 2001, Accepted March 5, 2001 |
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Keywords: | Matrix equation Symmetric positive semidefinite matrix Bisymmetric positive semidefinite matrix |
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