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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)

see also:


[Solutions]

  automatisch erstellt am 14. 10. 2004