The left and right inverse eigenvalue problems of generalized reflexive and anti-reflexive matrices

Authors:
Mao-lin Liang;Li-fang Dai
Affiliations:
School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, PR China;School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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An inverse eigenproblem and an associated approximation problem for generalized reflexive and anti-reflexive matrices

Journal of Computational and Applied Mathematics

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Abstract

Let nxn complex matrices R and S be nontrivial generalized reflection matrices, i.e., R^*=R=R^-^1+/-I"n, S^*=S=S^-^1+/-I"n. A complex matrix A with order n is said to be a generalized reflexive (or anti-reflexive ) matrix, if RAS=A (or RAS=-A). In this paper, the solvability conditions of the left and right inverse eigenvalue problems for generalized reflexive and anti-reflexive matrices are derived, and the general solutions are also given. In addition, the associated approximation solutions in the solution sets of the above problems are provided. The results in present paper extend some recent conclusions.