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{Mathematical Physics --- PHZ 3113}\\\vspace {2mm} 
Homework 10 (April 10, 2013) \\ Matrix Algebra
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\noindent 1. Find three $2\times 2$ matrices $\sigma_i$,
$i=1,2,3$, which fulfill the relations
\begin{eqnarray} 
  \sigma_i\,\sigma_j &=& i\,\epsilon_{ijk}\,\sigma_k
  ~~{\rm for}~~ i\ne j\,, \\
  \sigma_i\,\sigma_j + \sigma_j\,\sigma_i &=& 
  2\,\delta_{ij}\,1_2\,,
\end{eqnarray} 
where $1_2$ is the $2\times 2$ unit matrix.
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\noindent 2. Find the transformation, which generates the general
solution $\sigma'_i$, $i=1,2,3$ from your previous special solution.
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