The Wss P0 Matrix Completion Problem for Symmetric Patterns of Acyclic Digraphs of Order Four

Authors

  • Victor Tomno Moi University, Department of Mathematics and Physics. P.0. Box 3900-30100, Eldoret, Kenya
  • Fredrick Nyamwala Moi University, Department of Mathematics and Physics. P.0. Box 3900-30100, Eldoret, Kenya
  • Waweru Kamaku Jomo Kenyatta University of Agriculture and Technology, Department of Pure and Applied Mathematics. P.O. Box 6200-00200, Nairobi, Kenya

Keywords:

Acyclic digraphs, matrix completion, Partial matrix, Principal minor, symmetric patterns, weakly sign symmetric P0-matrix, Zero completion.

Abstract

In this paper we study weakly sign symmetric Wss P0-matrix specifying symmetric patterns of acyclic digraphs of 4 vertices where necessary and sufficient conditions for a digraphs to have weakly sign symmetric P0-matrix completion are stated and discussed. It is shown that all symmetric patterns specifying acyclic digraphs of order 4 with without an arc, 2 arcs and regular digraphs with 4 arcs have zero completion to weakly sign symmetric P0-matrix.

References

J.Y. Choi, L.M. Dealba, L. Hogben, M. Maxwell. “The -Matrix Completion Problem.” Electronic Journal of Linear Algebra, Vol. 9, PP. 1-20, 2002.

L. M. DeAlba, T.L. Hardy, L. Hogben and A. Wangsness. “The (Weakly) Sign Symmetric -matrix Completion Problems.” Electronic Journal of Linear Algebra, Vol. 10, PP. 257-271, 2003.

F. Harary. Graph Theory; New York; Addison-Wesley Publishing Company, 1969.

J.Y. Choi, L.M. Dealba, L. Hogben, B.M. Kivunge, S.K. Nordstrom and M. Shedenhelm. “The Nonnegative Matrix Completion Problem.” Electronic Journal of Linear Algebra, Vol. 10, PP. 46-59, 2003

L. Hogben. “Graph Theoretic Methods of Matrix Completion Problem.” Linear Algebra and its Applications, Vol. 328, PP. 161-202, 2001.

L. Hogben. “Matrix Completion Problems for pairs of related classes of matrices.” Linear Algebra and its Applications, Vol. 373, PP.13-29, 2003

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Published

2018-01-15

How to Cite

Tomno, V., Nyamwala, F., & Kamaku, W. (2018). The Wss P0 Matrix Completion Problem for Symmetric Patterns of Acyclic Digraphs of Order Four. International Journal of Sciences: Basic and Applied Research (IJSBAR), 37(1), 112–121. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/8591

Issue

Vol. 37 No. 1 (2018)

Section

Articles

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