On computing the maximum corank in the Frisch scheme

The paper concerns the Frisch scheme for identii-cation of linear relations from static noisy data. The central problem is, for a given non-singular nn noisy, linearly independent data covariance matrix n , determine the maximal corank of n ? n , and associated maximizers ? n , over the set of diagonal uncorre-lated additive noise covariance matrices n such that n n , i.e. such that n ? ? n is the covariance matrix of some real data satisfying a maximal number of linear relations. The key tools are results connecting the corank of partitioned sign-deenite matrices with their associated Schur complements. These are used to provide an alternative derivation of the well-known conditions for unity maximal corank and upper bounds on the maximal corank in the general case. A procedure for computation of the maximum is also proposed and its relation to the work of previous authors discussed. Finally, related results on a recursive approach to the problem are given.