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

README.md

This C++ program calculates the determinant, eigenvalues, and eigenvectors of a 2x2 matrix. Users can input the matrix elements, and the program performs the following tasks: Matrix Input and Display: ...
Example of solving for the eigenvalues of a 2x2 matrix.
The eigenvalue complementarity problem (EiCP) represents a class of mathematical challenges where the determination of eigenvalues and corresponding eigenvectors is constrained by complementarity ...
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 ...