fEigFac – IQClab

The function $[M,J,v,in]=fEigFac(P)$ factorizes the symmetric (or Hermitian) $P$ matrix as:

$P=M^TJM=M^T\left(\begin{array}{ccc}I_{n_+}&0&0\\0&0_{n_0}&0\\0&0& I_{n_-} \end{array}\right)M$

Here

$M$ is the outer factor
$J$ is the middle term
$v$ is the set of eigenvectors of P
$in$ is the vector $in=[n_+,n_0,n_-]$ , where $n_{+}$ , $n_0$ , and $n_{-}$ are the number of positive, zero, and negative eigenvalues respectively.