A new general form and the extremal rank of the centrosymmetric solutions to A1X=C1and A3XB3=C3 are derived.
ZHANG Xiang, HAO Lei, WANG Qing-wen
. Extremal Ranks of Centrosymmetric Solution to System of Matrix Equations[J]. Journal of Shanghai University, 2012
, 18(6)
: 596
-600
.
DOI: 10.3969/j.issn.1007-2861.2012.06.009
[1]MITRA S K. Fixed rank solutions of linear matix equations [J]. Sankhyā: The Indian Journal of Statistics, Series A (1961—2002), 1972, 34(4):387-392.
[2]MARSGLIA G, STYAN G P H. Equalities and inequalities for ranks of matrices [J]. Linear and Multilinear Algebra, 1974, 2(3):269-292.
[3]TIAN Y. Upper and lower bounds for ranks of matix expressions using generalized inverses [J]. Linear Algebra Appl, 2002, 355(1/2/3):187-214.
[4]TIAN Y. Ranks of solutions of matix equation AXB=C [J]. Linear and Multilinear Algebra, 2003, 51(2):111-125.
[5]WANG Q W. Bisymmetric and centrosymmetric solutions to systems of real quaternion matix equations [J]. Compute Math Appl, 2005, 49(5/6):641-650.
[6]WANG Q W, WU Z C, LIN C Y. Extremal ranks of a quatrnion matix expression subject to consistent systems of quaternion matix equations with applications [J]. Applied Mathematics and Computation, 2006, 182(2):1755-1764.
[7]DATTA L, MORGERA S D. On the reducibility of centrosymmetric matrices-Applications in engineering problems [J]. Circuits Systems Sig Proc, 1989, 8(1):71-96.
[8]WANG Q W. The general solution to a system of real quaternion matrix equations [J]. Comput Math Appl, 2005, 49(5/6):665-675.
[9]TIAN Y. The solvability of two linear matrix equations [J].〖JP〗 Linear and Multilinear Algebra, 2000, 48(2):123-147.