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TitleThe N-matrix completion problem under digraphs assumptions
Author(s)Araújo, C. Mendes
Torregrosa, Juan R.
Urbano, Ana M.
KeywordsPartial matrix
Matrix completion problems
completion problem
directed graphs
Issue date15-Mar-2004
JournalLinear Algebra and its Applications
CitationMendes Araújo, C., Torregrosa, J. R., & Urbano, A. M. (2004, March). The N-matrix completion problem under digraphs assumptions. Linear Algebra and its Applications. Elsevier BV.
Abstract(s)An $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the graph of its specified entries is an acyclic graph or a cycle. We also prove that there exists the desired completion for partial $N$--matrices such that in its associated graphs the cycles play an important role.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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