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Matrix inverse problem and its optimal approximation problem for R-skew symmetric matrices |
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| Authors: | Guang-Xin Huang Feng Yin Ling Chen |
| Institution: | a Key laboratory for Neuroinformation of Ministry of Education, School of Life Science and Technology, School of Applied Mathematics, University of Electronic Science and Technology, Chengdu 610054, China b College of Information and Management, Key laboratory of Geomathematics of Sichuan Province, Chengdu University of Technology, Chengdu, 610059, China c School of Science, Sichuan University of Science and Engineering, Zigong, 643000, China |
| Abstract: | Let R ∈ Cn×n be a nontrivial involution, i.e., R2 = I and R ≠ ±I. A matrix A ∈ Cn×n is called R-skew symmetric if RAR = −A. The least-squares solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are firstly derived, then the solvability conditions and the solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are given. The solutions of the corresponding optimal approximation problem with R∗ = R for R-skew symmetric matrices are also derived. At last an algorithm for the optimal approximation problem is given. It can be seen that we extend our previous results G.X. Huang, F. Yin, Matrix inverse problem and its optimal approximation problem for R-symmetric matrices, Appl. Math. Comput. 189 (2007) 482-489] and the results proposed by Zhou et al. F.Z. Zhou, L. Zhang, X.Y. Hu, Least-square solutions for inverse problem of centrosymmetric matrices, Comput. Math. Appl. 45 (2003) 1581-1589]. |
| Keywords: | R-skew symmetric matrix Matrix inverse problem Optimal approximation problem Least-squares solution Singular value decomposition (SVD) |
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