The copositive completion problem

Date
2005-10-01
Authors
Hogben, Leslie
Johnson, Charles
Reams, Robert
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Altmetrics
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Mathematics
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Abstract

An n × n real symmetric matrix A is called (strictly) copositive if xTAx ⩾ 0 (>0) whenever x ∈ Rn satisfies x ⩾ 0 (x ⩾ 0 and x ≠ 0). The (strictly) copositive matrix completion problem asks which partial (strictly) copositive matrices have a completion to a (strictly) copositive matrix. We prove that every partial (strictly) copositive matrix has a (strictly) copositive matrix completion and give a lower bound on the values used in the completion. We answer affirmatively an open question whether an n × n copositive matrix A = (aij) with all diagonal entries aii = 1 stays copositive if each off-diagonal entry of A is replaced by min{aij, 1}.

Description

This is a manuscript of an article from Linear Algebra and its Applications 408 (2005): 207, doi:10.1016/j.laa.2005.06.019. Posted with permission.

Keywords
Copositive, Strictly copositive, Matrix completion, Partial matrix
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