Nullities for a class of skew-symmetric Toeplitz band matrices
| Autor: | Mark Van Veen, John Greene, Ronald J. Evans |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Class (set theory) Algebra and Number Theory Band matrix Computation Directed graph Mathematics - Commutative Algebra Commutative Algebra (math.AC) 15A03 Toeplitz matrix Combinatorics Integer FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Skew-symmetric matrix Asymptotic formula Combinatorics (math.CO) Geometry and Topology Mathematics |
| Zdroj: | Linear Algebra and its Applications. 593:276-304 |
| ISSN: | 0024-3795 |
| Popis: | For all n > k ≥ 1 , we give formulas for the nullity N ( n , k ) of the n × n skew-symmetric Toeplitz band matrix whose first k superdiagonals have all entries 1 and whose remaining superdiagonals have all entries 0. This is accomplished by counting the number of cycles in certain directed graphs. As an application, for each fixed integer z ≥ 0 and large fixed k, we give an asymptotic formula for the percentage of n > k satisfying N ( n , k ) = z . For the purpose of rapid computation, an algorithm is devised that quickly computes N ( n , k ) even for extremely large values of n and k. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect