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Mathematics-Online lexicon:

Orthogonal and Special Orthogonal Group


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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