31 citations · 51 across the 2 of their papers we have counts for
Showing math.GMShow all
2 papers · 1 filter
math.GM2007★ 31 cited
Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations
Johan Ernest Mebius
The general 4D rotation matrix is specialised to the general 3D rotation matrix by equating its leftmost top element (a00) to 1. Its associate matrix of products of the left-hand a…
math.GM2005★ 20 cited
A matrix-based proof of the quaternion representation theorem for four-dimensional rotations
Johan Ernest Mebius
To each 4x4 matrix of reals another 4x4 matrix is constructed, the so-called associate matrix. This associate matrix is shown to have rank 1 and norm 1 (considered as a 16D vector)…