In applying statistical methods such as principal component analysis, canonical correlation analysis, and sufficient dimension reduction, we need to determine how many eigenvectors of a random matrix ...

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 ...