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

Abstract

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