Inverse eigenproblem of anti-symmetric and persymmetric matrices and its approximation

摘要

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_E~n. The best approximation problem associated with AS_E~n is discussed, that is: to find the nearest matrix to a given matrix A~* by A ∈ AS_E~n. The existence and uniqueness of the best approximation problem is proved and the expression of this nearest matrix is provided.