Ars Technica

Finding the Eigenvectors of a 2x2 Matrix in a Fragment Shader

Seems like GE on a 2x2 matrix should be pretty darn fast.... especially if you use scalar * vector type operations.
JSTOR Daily

The Expression for the Group Inverse of the Anti–triangular Block Matrix

Abstract. In this paper, we present the explicit expression for the group inverse of the sum of two matrices. As an application, the explicit expression for the group ...