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

F. Li & L. Lin

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

Published online: 2007-05

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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 \begin{equation}\label{eq1} H= \left [ \begin{array}{cc} H_{11}&H_{12}\\ H_{21}&H_{22} \end{array} \right ], \end{equation} 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.

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@Article{NM-16-131, author = {F. Li and L. Lin}, title = {A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {2}, pages = {131--139}, 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 \begin{equation}\label{eq1} H= \left [ \begin{array}{cc} H_{11}&H_{12}\\ H_{21}&H_{22} \end{array} \right ], \end{equation} 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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8051.html} }
TY - JOUR T1 - A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices AU - F. Li & L. Lin JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 131 EP - 139 PY - 2007 DA - 2007/05 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/nm/8051.html KW - AB - 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 \begin{equation}\label{eq1} H= \left [ \begin{array}{cc} H_{11}&H_{12}\\ H_{21}&H_{22} \end{array} \right ], \end{equation} 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.
F. Li & L. Lin. (1970). A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices. Numerical Mathematics, a Journal of Chinese Universities. 16 (2). 131-139. doi:
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