A recurrence relation for the product of the nonzero eigenvalues of singular symmetric Toeplitz matrices

The article presents an extension of a well-known recurrence relation for Toeplitz symmetric matrices to the case of incomplete rank matrices. It is shown that the product of the nonzero eigenvalues of the matrix of order p+1 can be obtained from the product of the non-zero eigenvalues of the matrix of order p, and the so-called minimum-norm prediction vector introduced by Kumaresan and Tufts (1982) in the context of parameter estimation.<
>