TITLE: Where can I calculate the exponential of a matrix online?
QUESTION [9 upvotes]: Where can I exponentiate a $3\times 3$ matrix like $\left[\begin{array}{ccc}
0 & 1 & 0\\
1 & 0 & 0\\
0 & 0 & 0
\end{array}\right]$
  online?
Is there some website where this is possible?
Thank you very much.

REPLY [2 votes]: Somewhat perversely, could I suggest you first try analytically, by Sylvester's formula, or, more specifically, simpler methods as below? 
Still, in your specific case, this would be overkill: your matrix is trivially diagonalizable,
$$M=\left[\begin{array}{ccc}
0 & 1 & 0\\
1 & 0 & 0\\
0 & 0 & 0
\end{array}\right]=\frac{1}{\sqrt2}\left[\begin{array}{ccc}
1 & 1 & 0\\
1 & -1 & 0\\
0 & 0 &  {\sqrt2}
\end{array}\right] ~~
\left[\begin{array}{ccc}
1 & 0 & 0\\
0 & -1 & 0\\
0 & 0 & 0
\end{array}\right]~\frac{1}{\sqrt2}\left[\begin{array}{ccc}
1 & 1 & 0\\
1 & -1 & 0\\
0 & 0 &  {\sqrt2}
\end{array}\right]\equiv R^{-1} D R,$$
for the obviously defined diagonal matrix D and diagonalizing rotations R.
It then immediately follows that 
$$
\exp M= R^{-1} e^D R=  \left[\begin{array}{ccc}
\cosh 1 & \sinh 1 & 0\\
\sinh 1 & \cosh 1 & 0\\
0 & 0 & 1
\end{array}\right].
$$
Sylvester's formula generalizes to non-diagonalizable matrices, but my sense is you are dealing with diagonalizable ones.