The solvability conditions for the inverse eigenvalue problem of Hermitian and generalized skew-Hamiltonian matrices and its approximation
Zheng‐Jian Bai · Inverse Problems · 2003
In this paper, we first consider the inverse eigenvalue problem as follows: find a matrix A with specified eigenpairs, where A is a Hermitian and generalized skew-Hamiltonian 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 S . Then we discuss the best approximation problem for the inverse eigenproblem. That is, given an arbitrary Ã, find a matrix A ∗ ∊ S 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.