Bounds for Eigenvalues of Hermitian Trench Matrices.
Abstract
A banded matrix H = (hij) to the Nth power i, j=O is one such that hij = O for j - i greater than r and for i - j greater than s, where r and s are nonnegative integers. In (5) W. F. Trench and I called it strictly banded if, in addition, r + s greater than or less than N. We also showed that a necessary condition for a strictly banded matrix to have a Toeplitz inverse is that it have a certain special structure fully characterized by two polynomials, A(x) of degree r and B(x) of degree s. I call a matrix having this special structure a Trench matrix. It was also shown in (5) that a Trench matrix is nonsingular if and only if A(x) and B(x) have no common zero, and that a strictly banded matrix has a Toeplitz inverse if and only if it is a nonsingular Trench matrix. In this paper there are established bounds for eigenvalues of Hermitian Trench matrices that depend only on the polynomials A(x) and B(x) and not on the order of the matrix. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA077122
Entities
People
- Thomas N.E. Greville
Organizations
- University of Wisconsin–Madison