Inverse Eigenvalue Problem of Unitary Hessenberg Matrices
Chunhong Wu, Linzhang Lu · Discrete Dynamics in Nature and Society · 2009
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 be a modified submatrix of Hk. It is shown that when the minimal and maximal eigenvalues of (k = 1, 2, …, n) are known, H can be constructed uniquely and efficiently. Theoretic analysis, numerical algorithm, and a small example are given.