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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 $ Q$ so that $ D=Q^{-1}B\,Q$ is diagonal. Give $ D$ explicitly.
(Authors: Walk/Höfert)

Solution:

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  automatisch erstellt am 14. 10. 2004