Believe it or not, computing the eigen-decomposition of a 2x2 symmetric matrix is not as trivial as it seems. While I was doing my M.Eng thesis, at a certain point I was implementing two algorithms:
-
the
eig_symm_*algorithm of the GNU Scientific Library. -
the closed-form algorithm described in:
Jim Blinn, "Consider the Lowly 2x2 Matrix", IEEE Computer Graphics and Applications, March 1996, pp. 82-88.
And I found bugs in both! GSL would fail on simple cases: for diagonal matrices it would return two equal eigen-vectors. Blinn's algorithm has a couple of minor bugs.
The source code presented here contains Blinn's algorithm with a couple of corrections.