# What is the exponential for the matrix

What is the exponential for the matrix

$$\begin{pmatrix} 0 & -x & 0 \\ x & 0 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix}$$

Is it $$\begin{pmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}$$

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A quick search would have answered your question for you. en.wikipedia.org/wiki/Matrix_exponential –  SyntacticSugar Oct 15 '13 at 3:59
@sarah: that is correct. –  Amzoti Oct 15 '13 at 4:25

Hint: Exponential of a matrix is defined using Taylor series, viz $$e^A=I+A+\frac12A^2+...=\sum_{n=1}\frac1{n!}A^n$$