Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Orthogonal and Special Orthogonal Group

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
The set of all orthogonal $ (n\times n)$-matrices $ Q$ is called orthogonal group $ O(n)$.

For $ Q\in O(n)$

$\displaystyle Q^{-1} = Q^{\operatorname t}\,, \quad \vert\operatorname{det}\,Q\vert=1 $

holds, and each coordinate transormation

$\displaystyle x \to x^\prime = Qx $

preserves length and scalar product.

The set of all orthogonal $ (n\times n)$-matrices $ Q$ with $ \operatorname{det} Q=1$ is called rotation group or special orthogonal group

$\displaystyle SO(n) \subset O(n) \, . $

(Authors: Höllig/Reble/Höfert)

see also:

  automatically generated 2/10/2005