Title :
A recurrence relation for the product of the nonzero eigenvalues of singular symmetric Toeplitz matrices
Author_Institution :
Dept. Signal, Telecom Paris, Paris, France
fDate :
6/1/1994 12:00:00 AM
Abstract :
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
Keywords :
determinants; eigenvalues and eigenfunctions; matrix algebra; parameter estimation; determinants; incomplete rank matrices; minimum-norm prediction vector; nonzero eigenvalues product; parameter estimation; recurrence relation; singular symmetric Toeplitz matrices; Autocorrelation; Eigenvalues and eigenfunctions; Parameter estimation; Polynomials; Symmetric matrices; Vectors;
Journal_Title :
Signal Processing, IEEE Transactions on
