Seems like GE on a 2x2 matrix should be pretty darn fast.... especially if you use scalar * vector type operations.
Mathematics of Computation, Vol. 23, No. 105 (Jan., 1969), pp. 119-125 (7 pages) Sets of simple matrices of order N are given, together with all of their eigenvalues and right eigenvectors, and simple ...
Eigensensitivity analysis addresses how the spectral properties of damped systems—specifically, the eigenvalues and eigenvectors—respond to variations in system parameters. This analytical approach is ...