See original work at https://www.mpi-hd.mpg.de/personalhomes/globes/3x3/.
A common scientific problem is the numerical calculation of the eigensystem of symmetric or hermitian 3x3 matrices. If this calculation has to be performed many times, standard packages like LAPACK, the GNU Scientific Library, and the Numerical Recipes Library may not be the optimal choice because they are optimized mainly for large matrices.
This is a C# port of the C implementations of several algorithms which were specifically optimized for 3x3 problems. All algorithms are discussed in detail in the following paper:
Joachim Kopp
Efficient numerical diagonalization of hermitian 3x3 matrices
Int.J.Mod.Phys.C 19 (2008) 523-548
arXiv.org: http://arxiv.org/abs/physics/0610206