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# Linear restriction problem of Hermitian reflexive matrices and its approximation.

College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China

Applied Mathematics and Computation (Impact Factor: 1.35). 01/2008; 200:341-351. DOI: 10.1016/j.amc.2007.11.020 Source: DBLP

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**ABSTRACT:**In this paper, The Hermitian reflexive solutions and the anti-Hermitian reflexive solutions of matrix equations AX = B, XC = D are considered. With special properties of partitioned matrices and Hermitian reflexive (anti-Hermitian reflexive) matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is considered.Energy Procedia 01/2012; 17:1591–1597. - [Show abstract] [Hide abstract]

**ABSTRACT:**A square matrix R is called a generalized reflection matrix iff R=R H and R 2 =I. Let P and Q be two generalized reflexion matrices. From the authors’ abstract: An n×n matrix A is said to be generalized reflexive (generalized anti-reflexive) with respect to the matrix pair (P,Q) if A=PAQ (A=-PAQ). It is obvious that any n×m matrix is also generalized reflexive with respect to the matrix pair (I n ,I m ). By extending the conjugate gradient least squares approach, the present paper treats two iterative algorithms to solve the sytem of matrix equations ℱ i (X)=A i ,i=1,2,⋯,m·Linear Algebra and its Applications 12/2012; 437(11):2793–2812. · 0.97 Impact Factor

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