@article {
author = {Nazari, Alimohammad and Nezami, Atiyeh},
title = {On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix},
journal = {Wavelet and Linear Algebra},
volume = {5},
number = {2},
pages = {15-20},
year = {2019},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {10.22072/wala.2018.87428.1174},
abstract = {This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = \begin{pmatrix} A & B \\ C & D_0 \end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$), in which $A \in \mathbb{C}^{n\times n}$ is invertible, $ B \in \mathbb{C}^{n\times m}, C \in \mathbb{C}^{m\times n}$ and $D \in \mathbb{C}^{m\times m}$ with $\rm {Rank\{G_D\}} < n+m-1$ and given eigenvalues of matrix $\mathcal{M} = D - C A^{-1} B $ as $z_1, z_2, \cdots, z_{m}$ where $|z_1|\ge |z_2|\ge \cdots \ge |z_{m-1}|\ge |z_m|$. Finally, an explicit formula is proven for spectral distance $G_D$ and $G_D_0$ which is expressed by the two last eigenvalues of $\mathcal{M}$.},
keywords = {Eigenvalues,Normal matrix,Distance norm},
url = {http://wala.vru.ac.ir/article_34905.html},
eprint = {http://wala.vru.ac.ir/article_34905_78e346b85c8a946b0f3cfa66d8b73fb8.pdf}
}