It seems like Boost doesn't support eigen-analysis, is that true?
Yes and no. Your described use case (2x2 and 3x3) is not well supported. However, there is the experimental "numeric-bindings" library in the boost-sandbox, that provides bindings against external libraries for eigenvalue computations like lapack, ACML or MKL. But honestly, I would try to avoid the dependence on such external libraries if all I want are the eigenvalues of 2x2 and 3x3 matrices.
Virtually all standard eigensolvers are designed for large matrices. For small, fixed size matrices, it is vastly more efficient in most cases to get eigenvalues/ vectors by direct solution of the characteristic polynomial (there are good algorithms for doing this in, e.g. NetLib). See, for example, this thread : http://www.groupsrv.com/science/about273201.html Matthias