Volume 16, Issue 2
A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 131-139

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• Abstract

Let $H \in {\mathbb C}^{n\times n}$ be an $n \times n$ unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition $H$ as $$\label{eq1} H= \left [ \begin{array}{cc} H_{11}&H_{12}\\ H_{21}&H_{22} \end{array} \right ],$$ where $H_{11}$ is its $k\times k$ leading principal submatrix; $H_{22}$ is the complementary matrix of $H_{11}$. In this paper, $H$ is constructed uniquely when its eigenvalues and the eigenvalues of $\widehat{H}_{11}$ and $\widehat{H}_{22}$ are known. Here $\widehat{H}_{11}$ and $\widehat{H}_{22}$ are rank-one modifications of $H_{11}$ and $H_{22}$ respectively.

• History

Published online: 2007-05

• Keywords