2024 : 11 : 13
Alimohammad Nazari

Alimohammad Nazari

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-3231-0340
Education: PhD.
ScopusId: 7003903991
HIndex:
Faculty: Science
Address: Arak University
Phone:

Research

Title
On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
Type
JournalPaper
Keywords
Eigenvalues Normal matrix Distance norm
Year
2018
Journal Wavelets and Linear Algebra
DOI
Researchers Alimohammad Nazari

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 $\mathcal{M}$.