Trigonometric functions of matrices: Difference between revisions

Revision as of 15:50, 2 March 2016

Revision as of 15:59, 2 March 2016

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\end{align}

</math>

For example, taking {{mvar|X}} to be a standard [[Pauli matrices|Pauli matrix]],

:<math>

\sigma_1 = \sigma_x =

\begin{pmatrix}

0&1\\

1&0

\end{pmatrix} ~,</math>

one has

:<math>

\sin(\theta \sigma_1) = \sin(\theta)~ \sigma_1 , \qquad \cos (\theta \sigma_1) = \cos (\theta)~I~.

</math>

{{see also| Axis–angle representation # Exponential map from so(3) to SO(3)}}