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

作者：Borobia Alberto^*; Canogar Roberto; Smigoc Helena

来源：Linear Algebra and Its Applications, 2010, 433(3): 606-617.

DOI：10.1016/j.laa.2010.03.025

• Matrix completions
• Inverse eigenvalue problems
• Matrices over integral domains

Let Lambda = {lambda(1), ..., lambda(n)}, n >= 2, be a given multiset of elements in an integral domain R and let P be a matrix of order n with at most 2n - 3 prescribed entries that belong to R. 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 R to obtain a matrix A with spectrum Lambda. We describe an algorithm to construct A. This result is an extension to integral domains of a classical completion result by Herskowitz for fields.

• 出版日期2010-9-1