I am using a fragment shader to, among other things, calculate the eigenvectors of a 2x2 matrix.I can calculate the eigenvalues just fine using the quadratic formula on the characteristic equation ...

This problem is known as order determination, and amounts to estimating the rank of a matrix. Previous order-determination procedures rely either on the decreasing pattern, or elbow, of the ...

Paul A. White, The Computation of Eigenvalues and Eigenvectors of a Matrix, Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 4 (Dec., 1958), pp. 393-437 ...