@MISC{MATRTOP3.MIZ,
  AUTHOR = {P\k{a}k, Karol},
  TITLE = {The Rotation Group},
  SECTION1 = {Preliminaries},
  SECTION2 = {Improper Rotation},
  SECTION3 = {Proper Rotation},
  SECTION4 = {Length-Preserving Linear Transformations},
  SECTION4 = {Rotation Matrix Classification},
  SECTION5 = {The Rotation Mapping a Given Point to Another Point},
  DAY = {30},
  MONTH = {May},
  YEAR = {2011},
  ADDRESS1 = {University of Bialystok, ul. Akademicka 2, 15-267 Bialystok},
  SUMMARY = {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.}}
