Matrix Transformations Help

**thelostchild** · July 7th 2008, 02:52 AM

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

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

many thanks

Simon

**Moo** · July 7th 2008, 02:59 AM

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 >.<

**bobak** · July 7th 2008, 07:32 AM

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

Thread: Matrix Transformations Help

LinkBack

Thread Tools

Display

Matrix Transformations Help

Similar Math Help Forum Discussions

Matrix Transformations

Matrix transformations

Matrix Transformations

Matrix transformations

Matrix Transformations

Search Tags