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Volume 23, Issue 1
On Solutions of Matrix Equation $AXA^T+BYB^T=C$

Yuan-Bei Deng & Xi-Yan Hu

J. Comp. Math., 23 (2005), pp. 17-26.

Published online: 2005-02

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  • 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.

  • Keywords

Matrix equation, Matrix norm, QSVD, Constrained condition, Optimal problem.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-23-17, author = {Yuan-Bei Deng and Xi-Yan Hu}, 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} }
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 -

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.

Yuan-Bei Deng and Xi-Yan Hu. (2005). On Solutions of Matrix Equation $AXA^T+BYB^T=C$. Journal of Computational Mathematics. 23 (1). 17-26. doi:
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