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- W1569702801 abstract "In this paper, the relationship between the (P,Q)-orthogonal symmetric and symmetric matrices is derived. By applying the generalized singular value decomposition, the general expression of the least square (P,Q)-orthogonal symmetric solutions for the matrix equation AT XB = C is provided. Based on the projection theorem in inner space, and by using the canonical correlation decomposition, an analytical expression of the optimal approximate solution in the least squares (P, Q)-orthogonal symmetric solution set of the matrix equation AT XB = C to a given matrix is obtained. An explicit expression of the least square (P, Q)-orthogonal symmetric solution for the matrix equation AT XB = C with the minimum-norm is also derived. An algorithm for finding the optimal approximation solution is described and some numerical results are given." @default.
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- W1569702801 date "2010-01-01" @default.
- W1569702801 modified "2023-09-23" @default.
- W1569702801 title "Least squares (P,Q)-orthogonal symmetric solutions of the matrix equation and its optimal approximation" @default.
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- W1569702801 doi "https://doi.org/10.13001/1081-3810.1392" @default.
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