Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Subject Areas : History and biography

A. Nazari ¹ , A. Nezami ²

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

Received: 2016-11-01 Accepted : 2017-04-18 Published : 2017-03-01

Keywords: Normal matrix, multiple eigenvalues, Singular value, distance matrices,

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 and‎assume that $\lambda$ is a given complex number‎‎that 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 multiple‎eigenvalue of matrix $\left(\begin{array}{cc}‎A & B \‎C & X‎ \end{array} \right)$‎. ‎We‎also find the nearest matrix $X$ to the matrix $D$‎.

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