Difference between revisions of "Rotation matrix"

Revision as of 23:50, August 25, 2011

A rotation matrix is an orthogonal n x n matrix having a determinant equal to 1.

The linear transformation T(x) = A x is a "rotation".

In two dimensions a rotation by $\theta$ can be represented by the matrix:

$R={\begin{pmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{pmatrix}}$

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-A '''rotation matrix''' is an orthogonal ''n x n'' [[matrix]] having a determinant equal to 1.
+A '''rotation matrix''' is an [[Orthogonal matrix| orthogonal]] ''n x n'' [[matrix]] having a determinant equal to 1.
 The linear transformation ''T('''x''')'' = ''A'' '''''x''''' is a "rotation".
+In two dimensions a rotation by <math>\theta</math> can be represented by the matrix:
+<math>  R = \begin{pmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{pmatrix}</math>
 [[Category:linear algebra]]