{"title":"Solving Linear Matrix Equations by Matrix Decompositions","authors":"Yongxin Yuan, Kezheng Zuo","volume":95,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1426,"pagesEnd":1430,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10000378","abstract":"
In this paper, a system of linear matrix equations
\r\nis considered. A new necessary and sufficient condition for the
\r\nconsistency of the equations is derived by means of the generalized
\r\nsingular-value decomposition, and the explicit representation of the
\r\ngeneral solution is provided.<\/p>\r\n","references":"[1] S. K. Mitra, Fixed rank solutions of linear matrix equations, Sankhya\r\nSer. A., 35 (1972) 387\u2013392.\r\n[2] S. K. Mitra, The matrix equation AX = C,XB = D, Linear Algebra\r\nand its Applications, 59 (1984) 171\u2013181.\r\n[3] F. Uhlig, On the matrix equation AX = B with applications to the generators\r\nof a controllability matrix, Linear Algebra and its Applications,\r\n85 (1987) 203\u2013209.\r\n[4] S. K. Mitra, A pair of simultaneous linear matrix equations A1XB1 =\r\nC1,A2XB2 = C2 and a matrix programming problem, Linear Algebra\r\nand its Applications, 131 (1990) 107\u2013123.\r\n[5] C. Y. Lin, Q. W. Wang, The minimal and maximal ranks of the general\r\nsolution to a system of matrix equations over an arbitrary division ring,\r\nMath. Sci. Res. J., 10 (2006) 57\u201365.\r\n[6] P. Bhimasankaram, Common solutions to the linear matrix equations\r\nAX = B,XC = D, and EXF = G, Sankhya Ser. 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