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 $D$.

**Keywords**

**Main Subjects**

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