Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 615069, 11 pages
doi:10.1155/2009/615069

Inverse eigenvalue problem of unitary Hessenberg matrices

Abstract

Let H∈ℂn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive, let Hk be the kth leading principal submatrix of H, and let H˜k be a modified submatrix of Hk. It is shown that when the minimal and maximal eigenvalues of H˜k (k=1,2,…,n) are known, H can be constructed uniquely and efficiently. Theoretic analysis, numerical algorithm, and a small example are given.