Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices

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• 作者：Vijay Higgins^a ; ^{higgins.v@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Charles Johnson^b ; ^{crjohn@wm.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A18 ; 15A42 ; 15B57
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：489
• 期：Complete
• 页码：104-122
• 全文大小：362 K

文摘

Which assignments from 2n−1$2n-1$ arbitrary, distinct real numbers as eigenvalues of designated leading principal submatrices permit a real symmetric tridiagonal matrix? We raise this question, motivated both by known results and recent work on multiplicities and interlacing equalities in symmetric matrices whose graph is a given tree. Known results are reviewed, a general conjecture is given, and several new partial results are proved.