Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/2870

 Title: The N-matrix completion problem under digraphs assumptions Author(s): Araújo, C. MendesTorregrosa, Juan R.Urbano, Ana M. Keywords: Partial matrixMatrix completion problemsN-matrixDigraphcompletion problemdirected graphs Issue date: 15-Mar-2004 Publisher: Elsevier Journal: Linear Algebra and its Applications Citation: Mendes 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. http://doi.org/10.1016/j.laa.2003.10.017 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. Type: Article URI: https://hdl.handle.net/1822/2870 DOI: 10.1016/j.laa.2003.10.017 ISSN: 0024-3795 Publisher version: www.sciencedirect.com Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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