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SUMMARYThe problem of generating a matrix A with speciÿed eigen-pair, where A is a symmetric and antipersymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by SAS n E . The optimal approximation problem associated with SAS n E is discussed, that is: to ÿnd the nearest matrix to a given matrix A * by A ∈ SAS n E . The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix.

The problem of generating a matrix A with specified eigenpair, where A is an anti-symmetric and persymmetric matrix, is presented. The solvability conditions are studied. A general expression of such a matrix is provided. We denote the set of such matrices by AS n E . The best approximation problem associated with AS n E is discussed, that is: to find the nearest matrix to a given matrix A * by A ∈ AS n E . The existence and uniqueness of the best approximation problem is proved and the expression of this nearest matrix is provided.

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