Why do I get negative eigenvalues for a sample covariance matrix in matlab?

Covariance matrices are positive semidefinite, thus have all positive eigenvalues (http://en.wikipedia.org/wiki/Positive-definite_matrix). Does this problem occur simply because the columns of the matrix are nearly linearly dependent? Is there anything I can do about this if a method I'm doing (involving matrix logs, matrix exponentials, and matrix^.5's) requires positive eigenvalues?