Browsing by Author "Kivunge, Benard"

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Bounds for the Second Largest Eigenvalue of Real 3 × 3 Symmetric Matrices with Entries Symmetric about the Origin
(2012) Barini, Geoffrey; Kivunge, Benard; Akanga, Jotham
Let ASn[a,b] denote a set of all real nxn symmetric matrices with entries in the interval [a,b]. In this article, we present bounds for the second largest eigenvalue λ2(A) of a real symmetric matrix A, such that A∈AS3 [-b,b].
THE M_0 – MATRIX COMPLETION PROBLEM FOR DIGRAPHS OF 5×5 MATRICES WITH LESS THAN FOUR DIRECTED LINES
(2013) Njoroge, James Mwangi; Kivunge, Benard; Muondwe, Samuel Kanyi; Kinyanjui, Anthony Muthondu
A real matrix is said to be – matrix if its principal minors are non - negative and all its non - diagonal entries are non - positive. In this project, we consider the – matrix completion problem. It is shown that any digraph with less than four directe d lines which is not a cycle has – completion. It is further shown that digraph of matrix with less than four directed lines which is a cycle does not have – completion.
On the cycle indices of frobenious groups
(2010) Munywoki, Michael; Kamuti, Ireri; Kivunge, Benard
There are several very useful formulas, which give the cycle indices of the binary operation of the sum, product, composition and po wer group of M and H in terms of cycle indices of M and H . One very useful binary operation on groups, which has not been exploited, is the semidirect product. Suppose G = M ⋊ H , a semi direct product; the question is: how can we express the cycle index of G in terms of the cycle indices of M and H ? This work partially answers this question by considering the cycle indices of so me particularly semidirect product groups; namely – Frobenious groups