@Article{JCM-23-17, author = {}, title = {On Solutions of Matrix Equation $AXA^T+BYB^T=C$}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {17--26}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8792.html} }