Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices

Abstract

In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectral behavior of the fractional powers of the rotation matrix by $\frac{\pi }{2}$ in ${\mathbb{R}}^3$ about some axis.

7 pages

References in corpus (1)

• Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations