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Mathematik-Online problems:

Problem 536: Orthogonal and Unitary Matrices


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 all orthogonal and unitary $ 2 \times 2$-matrices.

Hint: To find the unitary matrices use the attempt

$\displaystyle U=\left(
\begin{array}{rr}
a\,\mathrm{e}^{\mathrm{i}\varphi} & ...
...}^{\mathrm{i}\psi'} \\
\end{array}\right)\,, \qquad a,b,c,d\in \mathbb{R}\,,
$

and check the orthogonal condition of the columns.
(Authors: Höllig/Höfert)

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  automatisch erstellt am 12.  3. 2018