Abstract
In this article the (weakly) sign-symmetric \(\big [(w)ss\big ]\) \(Q_0\)-matrix completion problems are studied. Some necessary and sufficient conditions for a digraph to have the (w)ss \(Q_0\)-completion are given. Lastly the digraphs of order up to four having (w)ss \(Q_0\)-completion have been sorted out.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burg, J.P.: Maximum entropy spectral analysis. Ph.D. Dissertation. Dept. of Geophysics, Stanford University, Stanford, CA (1975)
Brualdi, R.A., Ryser, H.J.: Combinatorial Matrix Theory. Cambridge University Press, Cambridge (1991)
Choi, J.Y., DeAlba, L.M., Hogben, L., Kivunge, B., Nordstrom, S., Shedenhelm, M.: The nonnegative \(P_0\)-matrix completion problem. Electron. J. Linear Algebra 10, 46–59 (2003)
Choi, J.Y., DeAlba, L.M., Hogben, L., Maxwell, M.S., Wangsness, A.: The \(P_{0}\)-matrix completion problem. Electron. J. Linear Algebra 9, 1–20 (2002)
Dealba, L.M., Hardy, T.L., Hogben, L., Wangsness, A.: The (weakly) sign-symmetric \(P\)-matrix completion problems. Electron. J. Linear Algebra 10, 257–271 (2003)
Dealba, L.M., Hogben, L., Sarma, B.K.: The \(Q\)-matrix completion problem. Electron. J. Linear Algebra 18, 176–191 (2009)
Fallat, S.M., Johnson, C.R., Torregrosa, J.R., Urbano, A.M.: \(P\)-matrix completions under weak symmetry assumptions. Linear Algebra Appl. 312, 73–91 (2000)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
Hogben, L.: Graph theoretic methods for matrix completion problems. Linear Algebra Appl. 328, 161–202 (2001)
Hogben, L.: Matrix completion problems for pairs of related classes of matrices. Linear Algebra Appl. 373, 13–29 (2003)
Hogben, L.: Relationships between the completion problems for various classes of matrices. In: Proceedings of SIAM International Conference on Applied Linear Algebra (2003)
Hogben, L., Evers, J., Shane, S.: The positive and nonnegative \(P\)-matrix completion problems. http://www.math.iastate.edu/lhogben/research/nnP.pdf
Hogben, L., Wangsness, A.: Matrix completion problems. In: Hogben, L. (ed.) Handbook of Linear Algebra. Chapman and Hall/CRC Press, Boca Raton/London (2007)
Johnson, C.R., Kroschel, B.K.: The combinatorially symmetric \(P\)-matrix completion problem. Electron. J. Linear Algebra 1, 59–63 (1996)
Jordon, C., Torregrosa, J.R., Urbano, A.M.: Completions of partial \(P\)-matrices with acyclic or non-acyclic associated graph. Linear Algebra Appl. 368, 25–51 (2003)
Sarma, B.K., Sinha, K.: The positive \(Q\)-matrix completion problem. Discrete Math. Algorithms Appl. 7, 1–19 (2015)
Sarma, B.K., Sinha, K.: The nonnegative \(Q\)-matrix completion problem. J. Algebra Comb. Discrete Appl. 4, 61–74 (2016)
Sinha, K.: The weakly sign-symmetric \(Q\)-completion problem. Palestine J. Math. 5(1), 35–43 (2016)
Sinha, K.: The \(Q_1\)-completion problem. Malaya J. Math. 6(2), 443–450 (2018)
Sinha, K.: The non-negative \(Q_1\)-completion problem. Malaya J. Math. 7(4), 651–658 (2019)
Sinha, K.: The \(Q_0\)-matrix completion problem. Arab J. Math. Sci. (2019). https://doi.org/10.1016/j.ajmsc.2019.08.001
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sinha, K. A study on (weakly) sign-symmetric \(Q_0\)-matrix completion problems. Afr. Mat. 34, 65 (2023). https://doi.org/10.1007/s13370-023-01105-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13370-023-01105-0