Matrix Transformations Help

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July 7th 2008, 02:52 AM
thelostchild

Matrix Transformations Help

Sorry I'm new to this topic and attempting to self teach can anyone give me an idiots guide to this question

Quote:

The Matrix $\begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0\end{bmatrix}$ represents a rotation.

Find the equation of the axis of rotation and what is the angle of the rotation

(Headbang)

many thanks

Simon :)
July 7th 2008, 02:59 AM
Moo

Hello,

The axis is generated by the eigenvector associated to the eigenvalue 1.

$AX=X$

$\begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}=\begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}$

Solve for $x_1, ~x_2, ~x_3$

hmmm I'm sorry I don't remember how to find the angle >.<
July 7th 2008, 07:32 AM
bobak

This questions requires a decent 3D drawing.

Notice that $\begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} i\\j\\k \end{pmatrix}=\begin{pmatrix} k\\i\\j \end{pmatrix}$

Your swapping the axis around in order, so the line must be $\begin{pmatrix} 1\\1\\1 \end{pmatrix}$ and the angle is 120 degrees (as $A^3 = I$ )

Bobak

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