Differentiating the pseudo determinant

A class of derivatives is defined for the pseudo determinant Det(A) of a Hermitian matrix A. This class is shown to be non-empty and to have a unique, canonical member ∇Det(A)=Det(A)A+, where A+ is the Moore-Penrose pseudo inverse. The classic identity for the gradient of the determinant is thus reproduced. Examples are provided, including the maximum likelihood problem for the rank-deficient covariance matrix of the degenerate multivariate Gaussian distribution.