{"title":"The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem","authors":"Gu-Fang Mou, Ting-Zhu Huang","volume":50,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":124,"pagesEnd":129,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11521","abstract":"
An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.<\/p>\r\n","references":"[1] Gu-Fang Mou, Ting-Zhu Huang, The N10 -matrix completion problem, to\r\nappear.\r\n[2] T. Parthasathy, G. Ravindran, N-matrices, Linear Algebra Appl., 139\r\n(1990) 89-102.\r\n[3] Sheng-Wei Zhou, Ting-Zhu Huang, On Perron complements of inverse\r\nN0-matrices, Linear Algebra Appl., 434 (2011) 2081-2088.\r\n[4] L. DeAlba and L. Hogben, Completion problems of P-matrix patterns,\r\nLinear Algebra Appl., 319 (2000) 83-102.\r\n[5] S.M. Fallat, C.R. Johnson, J.R. Torregrosa and A.M. Urbano, P-matrix\r\ncompletions under weak symmetry assumptions, Linear Algebra Appl.,\r\n312 (2000) 73-91.\r\n[6] J. Bowers, J. Evers, L. Hogben, S. Shaner, K. Snider, and A. Wangsness,\r\nOn completion problems for various classes of P-matrices, Linear\r\nAlgebra Appl., 413 (2006) 342-354.\r\n[7] J.Y. Choi, L.M. DeAlba, L. Hogben, B. Kivunge, S. Nordstrom, and M.\r\nShedenhelm, The nonnegative P0 -matrix completion problem, Electronic\r\nJournal of Linear Algebra, 10 (2003) 46-59.\r\n[8] J.Y. Choi, L.M. DeAlba, L. Hogben, M. Maxwell and A. Wangsness, The\r\nP0-matrix completion problem, Electronic Journal of Linear Algebra, 9\r\n(2002) 1-20.\r\n[9] L. Hogben, Completions of M-matrix patterns, Linear Algebra Appl.,\r\n285 (1998) 143-152.\r\n[10] L. Hogben, Inverse M-matrix completions of patterns omitting some\r\ndiagonal positions, Linear Algebra Appl., 313 (2000) 173-192.\r\n[11] L. Hogben, The symmetric M-matrix and symmetric inverse M-matrix\r\ncompletion problems, Linear Algebra Appl., 353 (2002) 159-167.\r\n[12] C. Mendes Ara'ujo, J.R. Torregrosa and A.M. Urbano, N-matrix completion\r\nproblem, Linear Algebra Appl., 372 (2003) 111-125.\r\n[13] C. Mendes Ara'ujo, J.R. Torregrosa and A.M. Urbano, The N-matrix\r\ncompletion problem under digraphs assumptions, Linear Algebra Appl.,\r\n380 (2004) 213-225.\r\n[14] C. Mendes Ara'ujo, J.R. Torregrosa, A.M. Urbano, The symmetric Nmatrix\r\ncompletion problem, Linear Algebra Appl., 406 (2005) 235-252.\r\n[15] C. R. Johnson, M. Lundquist, T. J. Lundy, J. S. Maybee, Deterministic\r\ninverse zero-patterns, Diserete mathematics 113(2001) 211-236.\r\n[16] L. Hogben, Graph theoretic methods for matrix completion problems,\r\nLinear Algebra Appl., 328 (2001) 161-202.\r\n[17] Gray Chartrand, Ping Zhang, Introduction to graph theory, Published by\r\nthe McGraw-Hill Companies, Inc, 2005.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 50, 2011"}