Comment on "Order-recursive factorization of the pseudoinverse of a covariance matrix" [with reply]

Numerical counterexamples and theoretical analysis of the aforementioned paper are presented, and they show that the main result, Theorem 2, in the paper is incorrect. The original author's reply is also provided. The comment gives a counterexample to the previous paper, with which this author agrees. In this correction to that paper, it is shown that replacing "the pseudoinverse" with "a generalized inverse" and replacing Section II: Factor of a pseudoinverse of a covariance matrix with the new Section II as follows, corrects the problem and establishes a rigorous theory. Some examples are give to illustrate the theory and practice of the order-recursive procedure using g-inverses.