Abstract
The problem of generating a matrixA with specifiedeigenpair, where Ais an anti-symmetric and persymmetric matrix, is presented. Thesolvability conditions are studied. A general expression of such a matrixis provided. We denote the set of such matrices by \U0001d49c\U0001d4aeEn.The best approximation problem associated with \U0001d49c\U0001d4aeEnis discussed, that is: to find the nearest matrix to a given matrixA* by A ∊ \U0001d49c\U0001d4aeEn.The existence and uniqueness of the best approximation problem is proved andthe expression of this nearest matrix is provided.
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