线性流形上的广义反射矩阵反问题

Abstract

Abstract:

Let R ∈C^m×m and S ∈C^n×n be nontrivial unitary involutions, i.e., R^H=R=R^-1≠ ± I_m and S^H=S=S^-1≠ ± I_n. A ∈C^m×n is said to be a generalized reflexive matrixif RAS=A. This paper is concerned with the inverse problem for generalized reflexive matrices on a linear manifold and the optimal approximation to a given matrix. The general expression of the solutions of the problem is presented. Sufficient and necessary conditions for equations AX₂=Z₂, Y₂^HA=W₂^H having a common generalized reflexive matrix solution on the linear manifold are derived. The expression of the solution for relevant optimal approximation problem is given.

Key words: Inverse problem, Optimal approximation, Generalized reflexive matrix

CLC Number:

15A24

YUAN Yong-Xin, DAI Hua. Inverse Problems for Generalized Reflexive Matrices on a Linear Manifold[J].Acta mathematica scientia,Series A, 2009, 29(6): 1547-1560.

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Inverse Problems for Generalized Reflexive Matrices on a Linear Manifold

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