Mathematik-Online problems: Problem 79: Determination of Eigenvalues and Diagonalization

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematik-Online problems:
	Problem 79: Determination of Eigenvalues and Diagonalization

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

Find the eigenvalues of the matrix

$\displaystyle B =\left( \begin{array}{ccc} 1+4\alpha & 2\alpha & 0\\ 2\alpha &... ...lpha & 0\\ 0 & 0 & 1-\alpha \end{array} \right), \qquad \alpha \in \mathbb{R}$

dependent on $\alpha$ , and find an orthogonal matrix

so that $D=Q^{-1}B\,Q$ is diagonal. Give

explicitly.

(Authors: Walk/Höfert)

see also:

Keyword: Matrix: normal form
Keyword: Eigenvalue
Keyword: Eigenvector

[Solutions]

automatisch erstellt am 14. 10. 2004