By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-sq...By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.展开更多
In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied...In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.展开更多
基金The Project supported by Scientific Research Fund of Hunan Provincial Education Department,by National Natural Science Foundation of China (10171031)by Natural Science Fundation of Hunan Province (03JJY6028).
文摘By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution ^-X, which is both a least-squares symmetric orthogonal anti-symmetric solu- tion of the matrix equation A^TXA = B and a best approximation to a given matrix X^＊. Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
文摘In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.
