Spectrally arbitrary ray patterns
- 作者：Judith J. McDonald ; Jeffrey Stuart
- 关键词：Spectrally arbitrary ; Ray pattern
- 刊名：Linear Algebra and its Applications
- 出版年：2008
- 期刊代码：38_00243795
- 类别：mt
- 出版时间：1 August 2008
- 卷：429
- 期：4
- 页码：727-734
- 文件大小：116 K
摘要
An n×n ray pattern A is said to be spectrally arbitrary if for every monic nth degree polynomial f(x) with coefficients from 
, there is a matrix in the pattern class of A such that its characteristic polynomial is f(x). In this article the authors extend the nilpotent-Jacobi method for sign patterns to ray patterns, establishing a means to show that an irreducible ray pattern and all its superpatterns are spectrally arbitrary. They use this method to establish that a particular family of 160ae7" title="Click to view the MathML source" alt="Click to view the MathML source">n×n irreducible ray patterns with exactly 3n nonzeros is spectrally arbitrary. They then show that every n×n irreducible, spectrally arbitrary ray pattern has at least 3n-1 nonzeros.