Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem

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• 作者：C.R. Johnson^a ; ^{crjohn@wm.edu" class="auth_mail" title="E-mail the corresponding author} ; C. Marijuá ; n^b ; ^{marijuan@mat.uva.es" class="auth_mail" title="E-mail the corresponding author} ; M. Pisonero^c ; ^{mpisoner@maf.uva.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A18 ; 15A29 ; 15A42
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：512
• 期：Complete
• 页码：129-135
• 全文大小：250 K

文摘

A method is developed to show that certain spectra cannot be realized for the S-NIEP. It is applied in the 5-by-5 case to rule out many spectra that were previously unresolved. These are all in the case of 3 positive and 2 negative eigenvalues as all other cases are now resolved. For spectra of the sort we discuss, a diagram is given of the spectra that are excluded here, as well as those trivially realizable, those realizable because of the trace 0 case and those that may also be excluded because of the J–L–L conditions. A small region remains unresolved; it is a very small fraction of the area of those spectra we consider.