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On sequences of Toeplitz matrices over finite fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Price, Geoffrey L. Wortham, Myles |
| Copyright Year | 2018 |
| Abstract | Abstract For each non-negative integer n let A n be an n + 1 by n + 1 Toeplitz matrix over a finite field, F, and suppose for each n that A n is embedded in the upper left corner of A n + 1 . We study the structure of the sequence ν = { ν n : n ∈ Z + } , where ν n = null ( A n ) is the nullity of A n . For each n ∈ Z + and each nullity pattern ν 0 , ν 1 , … , ν n , we count the number of strings of Toeplitz matrices A 0 , A 1 , … , A n with this pattern. As an application we present an elementary proof of a result of D. E. Daykin on the number of n × n Toeplitz matrices over G F ( 2 ) of any specified rank. |
| Starting Page | 63 |
| Ending Page | 80 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.laa.2018.09.013 |
| Volume Number | 561 |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1804.00983 |
| Alternate Webpage(s) | https://doi.org/10.1016/j.laa.2018.09.013 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
