I'm trying to create a program, that will decompose a matrix using the Cholesky decomposition.

The decomposition itself isn't a difficult algorithm, but a matrix, to be eligible for Cholesky decomposition, must be symmetric and positive-definite. Checking whether a matrix is symmetric is easy, but the positive part proves to be more complex.

I've read about the Sylvester's criterion, but that leads to determinants, and based on what I found on the web, those are quite extensive and hard on computers.

In a nutshell - is there something I might be missing? Due to the fact the the matrix is square or something like that, is there possibly a simpler way to determine whether it's positive?

Regards, Paul