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Let $w>0$.compute the matrix $e^{A}$,where $$A=\begin{bmatrix} 0 & w \\ -w& 0 \\ \end{bmatrix}$$

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marked as duplicate by zhoraster, Henrik, mfl, rschwieb, Arnaud D. Dec 14 '16 at 19:55

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    $\begingroup$ Simplest approach is to find a quadratic equation for the matrix $A$, and then use this to simplify the Taylor series definition of $e^A$. $\endgroup$ – Semiclassical Dec 12 '16 at 5:39
  • $\begingroup$ Hint: $A=wX$ with $$X=\pmatrix{0&1\cr-1&0\cr}.$$ Computing the powers $X,X^2,X^3,X^4$ first will help you see the light. $\endgroup$ – Jyrki Lahtonen Dec 12 '16 at 5:54
  • $\begingroup$ thanks...by using your logic i solved it. $\endgroup$ – MatheMagic Dec 12 '16 at 6:56
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let $A=wX$, where $X=\pmatrix{0&1\cr-1&0\cr}$ and $w>0$.Now on expanding we will get $e^{A}$=$I(\cos w)+X(\sin w)$ which will ultimately give $$e^{A}=\begin{bmatrix} \cos w & \sin w \\ -\sin w& \cos w \\ \end{bmatrix}$$

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