A matrix completion problem over integral domains: the case with 2n-3 prescribed entries

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• 作者：Alberto Borobia ; Roberto Canogar ; Helena Š ; migoc
• 关键词：Matrix completions ; Inverse eigenvalue problems ; Matrices over integral domains
• 刊名：Linear Algebra and its Applications
• 出版年：2010
• 出版时间：1 September 2010
• 年：2010
• 卷：433
• 期：3
• 页码：606-617
• 全文大小：165 K

文摘

Let Λ={λ₁,…,λ_n}, n2, be a given multiset of elements in an integral domain and let P be a matrix of order n with at most 2n-3 prescribed entries that belong to . Under the assumption that each row, each column and the diagonal of P have at least one unprescribed entry, we prove that P can be completed over to obtain a matrix A with spectrum Λ. We describe an algorithm to construct A. This result is an extension to integral domains of a classical completion result by Herskowitz for fields.