I was wondering if anybody could help me understand the "double rotations" in 4-space. These are evidently rotations that fix only a single point--the center of rotation--and that take place in two hyperplanes simultaneously and independently.(adsbygoogle = window.adsbygoogle || []).push({});

Beyond that, I have an even more specific question. Suppose R1, R2, ..., Rn, where n is even, are reflections of 4-space in hyperplanes *through the origin*. Under what conditions is the product a "double rotation"? It's clear the result is a rotation of some kind: first, the products R1 * R2, R3 * R4, ... are each individually rotations; second, the product of two rotations fixing the origin will be another rotation fixing the origin (I don't think this is obvious since in 4-space the product of two rotations is not necessarily a rotation, but I've worked out a simple proof using quaternions).

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Double rotations in 4-space

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Double rotations space | Date |
---|---|

A Example of how a rotation matrix preserves symmetry of PDE | Feb 10, 2018 |

A 4th order tensor inverse and double dot product computation | May 10, 2017 |

I A double in this example problem | Aug 28, 2016 |

Diff eqs with eigenvectors: double roots, but 2nd eigenvector? | Nov 15, 2015 |

Double Summation | Jun 28, 2015 |

**Physics Forums - The Fusion of Science and Community**