Logarithm of a matrix: Difference between revisions

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<math>
\sum_{k=0}^\infty{1 \over k!}B_n^k =\begin{pmatrix}
\sum_{k=0}^\infty{(-1)^k \over 2k!}(\alpha+2\pi n)^{2k} & -\sum_{k=0}^\infty{(-1)^k \over (2k+1)!}(\alpha+2\pi n)^{2k+1} \\
\sum_{k=0}^\infty{(-1)^k \over (2k+1)!}(\alpha+2\pi n)^{2k+1} & \sum_{k=0}^\infty{(-1)^k \over 2k!}(\alpha+2\pi n)^{2k} \\
\end{pmatrix} =\begin{pmatrix}
\cos(\alpha) & -\sin(\alpha) \\
\sin(\alpha) & \cos(\alpha) \\
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