Spectrally arbitrary pattern extensions

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• 作者：In-Jae Kim^a ; ^{in-jae.kim@mnsu.edu} ; Bryan L. Shader^b ; ^{bshader@uwyo.edu} ; Kevin N. Vander Meulen^c ; ^{kvanderm@redeemer.ca} ; Matthew West^c ; ¹ ; ^{matthewmcwest@gmail.com}
• 关键词：15A18 ; 15A29 ; 15B35
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：517
• 期：Complete
• 页码：120-128
• 全文大小：335 K
• 卷排序：517

文摘

A matrix pattern is often either a sign pattern with entries in {0,+,−}{0,+,−} or, more simply, a nonzero pattern with entries in {0,⁎}{0,⁎}. A matrix pattern AA is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix having the pattern AA and the chosen spectrum. We describe a graphical technique, a triangle extension, for constructing spectrally arbitrary patterns out of some known lower order spectrally arbitrary patterns. These methods provide a new way of viewing some known spectrally arbitrary patterns, as well as providing many new families of spectrally arbitrary patterns. We also demonstrate how the technique can be applied to certain inertially arbitrary patterns to obtain larger inertially arbitrary patterns. We then provide an additional extension method for zero–nonzero patterns, patterns with entries in {0,⁎,⊛}{0,⁎,⊛}.