Rank-Preserving Extensions of Band Matrices

摘要

The existence of rank-preserving extensions of a band matrix is analyzed; necessary and sufficient conditions for a unique rank-preserving extension are given. As a corollary, we give a new characterization of, and formula for, the autocorrelation matrix of a stationary stochastic process in the case when the power spectrum consists of pure line spectra. Other applications are given to the problems of unitary or contractive extensions of a triangular matrix. Keywords: Reprints; Signal processing; Autocorrelation matrix; Toeplitz matrix; Band matrix; Rank-preserving extensions; Unitary extensions; Extensions to contractions; Matrix theory. (kr)