Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/2873

 Title: The symmetric N-matrix completion problem Author(s): Araújo, C. MendesTorregrosa, Juan R.Urbano, Ana M. Keywords: Partial matrixMatrix completion problemsN-matrixUndirected graphscompletion problemundirected graph Issue date: 1-Sep-2005 Publisher: Elsevier Journal: Linear Algebra and its Applications Citation: Araújo, C. M., Torregrosa, J. R., & Urbano, A. M. (2005, September). The symmetric N-matrix completion problem. Linear Algebra and its Applications. Elsevier BV. http://doi.org/10.1016/j.laa.2005.04.008 Abstract(s): An $n\times n$ matrix is called an $N$-matrix if all its principal minors are negative. In this paper, we are interested in the symmetric $N$-matrix completion problem, that is, when a partial symmetric $N$-matrix has a symmetric $N$-matrix completion. Here, we prove that a partial symmetric $N$-matrix has a symmetric $N$-matrix completion if the graph of its specified entries is chordal. Furthermore, if this graph is not chordal, then examples exist without symmetric $N$-matrix completions. Necessary and sufficient conditions for the existence of a symmetric $N$-matrix completion of a partial symmetric $N$-matrix whose associated graph is a cycle are given. Type: Article URI: https://hdl.handle.net/1822/2873 DOI: 10.1016/j.laa.2005.04.008 ISSN: 0024-3795 Publisher version: https://www.sciencedirect.com/science/article/pii/S0024379505002338 Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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