The Hurwitz Matrix Equations and Multifour Groups.
The importance of each node in a structure of links: Google-PageRank.
The Indecomposable Representations of the Dihedral 2-Groups.
The inertia of Hermitian tridiagonal block matrices.
The inertia set of nonnegative symmetric sign pattern with zero diagonal
The inertia set of a symmetric sign pattern is the set , where denotes the inertia of real symmetric matrix , and denotes the sign pattern class of . In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns with zero diagonal that require...
The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub.
The inverse eigenvalue and inertia problems for minimum rank two graphs.
The inverse of the Pascal lower triangular matrix modulo .
The Jordan forms of and .
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The Laplacian permanental polynomial for trees
The Laplacian spectrum of some digraphs obtained from the wheel
The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.
The Laplacian spread of graphs
The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected -cyclic graphs with vertices and Laplacian spread are discussed.
The Laplacian spread of tricyclic graphs.
The Largest Subdeterminant of a Matrix
The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...
The Legendre Formula in Clifford Analysis
2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.
The linear independence of sets of two and three canonical algebraic curvature tensors.
The matrix equation and related problems.
The maximal and minimal ranks of with applications.