TY - JOUR
T1 - On Solutions of Matrix Equation $AXA^T+BYB^T=C$
AU - Yuan-Bei Deng & Xi-Yan Hu
JO - Journal of Computational Mathematics
VL - 1
SP - 17
EP - 26
PY - 2005
DA - 2005/02
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8792.html
KW - Matrix equation, Matrix norm, QSVD, Constrained condition, Optimal problem.
AB - <p style="text-align: justify;">By making use of the quotient singular value decomposition (QSVD) of a matrix pair, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation $AXA^T+BYB^T=C$ with the unknown $X$ and $Y$, which may be both symmetric, skew-symmetric, nonnegative definite , positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.</p>