The left and right inverse eigenvalue problems of generalized reflexive and anti-reflexive matrices |
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Authors: | Mao-lin Liang Li-fang Dai |
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Affiliation: | School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, PR China |
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Abstract: | Let n×n complex matrices R and S be nontrivial generalized reflection matrices, i.e., R∗=R=R−1≠±In, S∗=S=S−1≠±In. 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. |
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Keywords: | Generalized reflexive (anti-reflexive) matrices Left and right eigenpairs Inverse eigenvalue problem Optimal approximation |
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