# Let $w>0$.compute the matrix $e^{A}$. [duplicate]

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

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

• Simplest approach is to find a quadratic equation for the matrix $A$, and then use this to simplify the Taylor series definition of $e^A$. – Semiclassical Dec 12 '16 at 5:39
• 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. – Jyrki Lahtonen Dec 12 '16 at 5:54
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 $$e^{A}=\begin{bmatrix} \cos w & \sin w \\ -\sin w& \cos w \\ \end{bmatrix}$$