I have a $N\times D$ matrix, where $N<D$.
I wish to compute the eigenvalues and eigenvectors of $X^TX$, which is a $D\times D$ matrix. To speedup the MATLAB computations, I want to compute instead for $XX^T$, a $N\times N$ matrix. It is indeed quite fast, and I obtain $V$, whose each column is an eigenvector for $XX^T$, and $D$, a diagonal matrix holding $XX^T$'s eigenvalues.
How do I go from $V$ and $D$ to the eigenvalues and eigenvectors of $X^TX$?