Document Type: Research Paper

Authors

Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran

Abstract

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $A\in\mathbb{C}^{n\times n}$‎ ‎and $D\in\mathbb{C}^{m\times m}$ and let the matrix $\left(\begin{array}{cc}‎ A & B \‎ C & D‎ \end{array} \right)$ be a normal matrix and‎ assume that $\lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to the set of matrices $X \in C^{m \times m}$ such that‎, ‎$\lambda$ be a multiple‎ eigenvalue of matrix $\left(\begin{array}{cc}‎ A & B \‎ C & X‎ \end{array} \right)$‎. ‎We‎ also find the nearest matrix $X$ to the matrix $D$‎.

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