TY - JOUR
A2 - Zhang, Yang
AU - Dong, Chang-Zhou
AU - Wang, Qing-Wen
AU - Zhang, Yu-Ping
PY - 2012
DA - 2012/12/20
TI - On the Hermitian -Conjugate Solution of a System of Matrix Equations
SP - 398085
VL - 2012
AB - Let R be an n by n nontrivial real symmetric involution matrix, that is,R=R−1=RT≠In. An n×n complex matrix A is termed R-conjugate ifA¯=RAR, where A¯ denotes the conjugate of A. We give necessary and sufficientconditions for the existence of the Hermitian R-conjugate solution to the systemof complex matrix equations AX=CandXB=D and present an expression ofthe Hermitian R-conjugate solution to this system when the solvability conditionsare satisfied. In addition, the solution to an optimal approximation problem isobtained. Furthermore, the least squares Hermitian R-conjugate solution with theleast norm to this system mentioned above is considered. The representation ofsuch solution is also derived. Finally, an algorithm and numerical examples aregiven.
SN - 1110-757X
UR - https://doi.org/10.1155/2012/398085
DO - 10.1155/2012/398085
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -