Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10997862 | Linear Algebra and its Applications | 2019 | 17 Pages |
Abstract
For each non-negative integer n let An be an n+1 by n+1 Toeplitz matrix over a finite field, F, and suppose for each n that An is embedded in the upper left corner of An+1. We study the structure of the sequence ν={νn:nâZ+}, where νn=null(An) is the nullity of An. For each nâZ+ and each nullity pattern ν0,ν1,â¦,νn, we count the number of strings of Toeplitz matrices A0,A1,â¦,An with this pattern. As an application we present an elementary proof of a result of D. E. Daykin on the number of nÃn Toeplitz matrices over GF(2) of any specified rank.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Geoffrey Price, Myles Wortham,