Any singular covariance matrix is pivoted so that the first diagonal partition is nonsingular and well-conditioned.
From the en.wikipedia.org
If the matrix is singular, then an LU factorization may still exist.
From the en.wikipedia.org
It is a consequence of the irreversibility or singular nature of the general transition matrix.
From the en.wikipedia.org
The transfer operator approach is very simple to implement, they say, requiring only singular vector computations of a matrix of transitions induced by the dynamics.
From the sciencedaily.com
The singular value decomposition and polar decomposition are matrix decompositions closely related to these geometric observations.