Mathematik-Online problems: Problem 565: Eigenvalue Problem with Parameter, Taylor expansion

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	Mathematik-Online problems:
	Problem 565: Eigenvalue Problem with Parameter, Taylor expansion

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Consider the eigenvalue problem

$\displaystyle \begin{pmatrix}0 & 1 & \varepsilon \\ 0 & 0 & 1 \\ 1 & \varep... ...lon)= \lambda(\varepsilon) v(\varepsilon), \quad \vert v(\varepsilon)\vert=1.$

a): Find the eigenvector corresponding to the eigenvalue $\lambda(0)=1$ .
b): Expand $\lambda$ as a function in $\varepsilon$ , up to terms of second order.
c): Use the expansion of $\lambda$ to find an expansion of $v(\varepsilon)$ .

(Authors: Höllig/Höfert)

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automatisch erstellt am 18. 1. 2017