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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