We introduce length-preserving linear transformations of Euclidean topological spaces. We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation). We show that every rotation that preserves orientation can be represented as a composition of base proper rotations. And finally, we show that every rotation that reverses orientation can be represented as a composition of proper rotations and one improper rotation.
@article{bwmeta1.element.doi-10_2478_v10037-012-0004-2,
author = {Karol P\k ak},
title = {The Rotation Group},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {23-29},
zbl = {1276.51005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0004-2}
}
Karol Pąk. The Rotation Group. Formalized Mathematics, Tome 20 (2012) pp. 23-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0004-2/
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