A RECURRENCE RELATION FOR THE PRODUCT OF THE NONZERO EIGENVALUES OF SINGULAR SYMMETRICAL TOEPLITZ MATRICES

This communication presents an extension of a well-known recurrence re lation for Toeplitz symmetric matrices to the case of incomplete rank matrices. It is shown that the product of the nonzero eigenvalues of t he matrix of order p + 1 can be obtained from the product of the non-z ero eigenvalues of the matrix of order p and the so-called minimum-nor m prediction vector introduced by Kumaresan and Tufts in the context o f parameter estimation.