Shouldn't the Laplace operator be positive definite?

[avaruuser]

Hello everyone,

I want to solve a Poisson equation to obtain the curl-free potential of the Helmholtz decomposition of a vector field defined on a mesh using sksparse's sparse Cholesky decomposition. The Cholesky decomposition requires the Laplacian to be symmetric positive definite, which I believe it should always be. I understand that the discrete Laplacian returned by igl.cotmatrix() should be negative semi-definite. However, the discrete negative laplacian obtained with igl.cotmatrix() from the cow and bunny meshes are symmetric but not positive definite. What am I getting wrong here?