The Solvability Conditions for the Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian Matrices and Its Approximation
نویسنده
چکیده
In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigen-pairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by LS . Then the best approximation problem for the inverse eigenproblem is discussed. That is: Given an arbitrary Ã, find a matrix A∗ ∈ LS which is nearest to à in the Frobenius norm. We show that the best approximation is unique and provide an expression for this nearest matrix.
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