Xi-Yan Hu
Abstract
Using the guotient singular value decomposition (QSVD) of a matrix pair [A,B], this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation (A~TXA,B~TXB)=(C,D).
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Using the guotient singular value decomposition (QSVD) of a matrix pair [A,B], this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation (A~TXA,B~TXB)=(C,D).
Key concepts: Skew-symmetric matrix, Mathematics, Matrix (chemical analysis), Symmetric matrix, Skew, Singular value decomposition, Positive-definite matrix, Mathematical analysis