while reading this article I came across following:
$[C]$ is a symmetric and not positive definite matrix. However a positive definite matrix $[C']$ can be obtained by equation:
$[C'] = [\phi]*[\lambda '] * [\phi]^{T}$
$[\phi]$ is the square matrix consisting of the eigenvectors of $[C]$. $[\lambda ']$ is the diagonal matrix containing the eigenvalues of $[C]$, however all negative eigenvalues are set to zero.
The result is the matrix $[C']$ which is positive definite.
Why does this work?