I am doing some signal processing and it should be that my matrix is positive definite as it is an auto-correlation matrix. However, which is the quickest way to check this? What are other people doing? Does Eigen have an API that could check?

I thought of this, but not sure how quick this is going to be:

http://en.wikipedia.org/wiki/Sylvester%27s_criterion

Thanks for any tips.

That depends on what you want to do with your matrix and what is the size of the matrix. If you want to solve a Ax=b problem, then you try to factorize it assuming it is SPD (e.g., using http://eigen.tuxfamily.org/dox/classEigen_1_1LLT.html) and then check that everything went well with the .info() method, or compute its eigen values with http://eigen.tuxfamily.org/dox/classEig ... olver.html and check that eigenvalues()(0)>0 && eigenvalues()(0)/eigenvalues()(n-1) > machine_precision.