Showing papers in "Linear Algebra and its Applications in 2012"

TL;DR: In this paper, a spectral theory of uniform hypergraphs is presented, which closely parallels Spectral Graph Theory (SG Theory), and a number of natural analogies of basic results in SG Theory are established.

TL;DR: In this paper, a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane is proposed.

TL;DR: In this article, a tensor-like combination of a Steiner system and a regular simplex is proposed to construct equiangular tight frames, which is valid in both real and complex settings, and shows that many of the few previously known examples of ETFs are but the first representatives of infinite families of such frames.

TL;DR: In this paper, the Wong sequences of subspaces are investigated and invoked to decompose the K n into V � ⊕ W �, where any bases of the linear spaces V � and W transform the matrix pencil into the Quasi-Weierstras form.

TL;DR: In this paper, the automorphism group on the second cohomology space is used to classify six-dimensional nilpotent Lie algebras over an arbitrary field.

TL;DR: In this paper, it was shown that the Moore-Penrose inverse, the author's pseudo-inverse, Chipman's weighted inverse and the Bott-Duffin inverse are all special cases of the more general class of (b, c ) -inverses.

TL;DR: It is shown that computing this quantity is equivalent to a problem in polyhedral combinatorics, and fully characterize its computational complexity, which sheds new light on the nonnegative rank problem, and allows for new improved lower bounds based on its geometric interpretation.

TL;DR: In this paper, the vertex spread of the zero forcing number and edge spreads for minimum rank/maximum nullity and zero forcing numbers are introduced and properties of the spreads are established and used to determine values of the minimum rank or maximum nullity for various types of grids with a vertex or edge deleted.

TL;DR: In this article, the adjacency, incidence and Laplacian matrices of a complex unit gain graph are studied and eigenvalue bounds for the adjACency matrix are derived.

TL;DR: It is shown that for general linearly converging stationary iterative schemes and general adaptation processes—which can be seen as a modification or perturbation of the iteration—the interlaced procedure still converges.

TL;DR: In this article, the exponential stability problem for a class of linear systems with time-varying delay is addressed, where the time delay is assumed to be a continuous function belonging to a given interval and not necessary to be differentiable.

TL;DR: This work presents a one-parameter family of divergence functions for measuring distances between Hermitian positive-definite matrices, and studies the invariance properties of these divergence functions as well as the matrix means based on them.

TL;DR: In this paper, Nikiforov showed that if G has no 4-cycle, then ρ 2 - ρ - ( n - 1 ) ⩽ 0, with equality if and only if G is the friendship graph.

TL;DR: In this paper, the M -coronal of a graph matrix M is introduced, where the matrix is associated with a graph in a prescribed way, and then it is used to compute the signless Laplacian spectrum of G 1 ∘ G 2 and G 1 ♢ G 2 in terms of the signedless L 1 spectrum of g 1 and g 2, respectively.

TL;DR: An iterative procedure is proposed which allows the computation of an accurate dominant SVD using multiple passes through A and an analysis of the convergence of this iteration and empirical demonstration of the proposed method on both synthetic and benchmark data are provided.

TL;DR: The zero forcing number of a graph is the minimum size of a zero forcing set as discussed by the authors, which is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity.

TL;DR: In this article, the authors give a description of Lie derivations of generalized matrix algebras and show how to obtain a Lie derivation of a generalized matrix algebra from a full matrix algebra.

TL;DR: In this paper, the spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs, and an analogue of the Perron-Frobenius theorem is proposed.

TL;DR: In this article, Mursaleen and Noman characterized some classes of compact operators on the difference sequence spaces c 0 λ( Δ ) and l ∞ λ ( Δ ) by using the Hausdorff measure of noncompactness.

TL;DR: In this article, the authors introduced the notion of multiplicative Lie n-derivation of a ring, generalizing the concept of a Lie triple derivation, and considered the question of when all multiplicative lie n-divergences of a triangular ring T have the so-called standard form.

TL;DR: Some Hermite-Hadamard type inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given in this paper, and applications in relation with the celebrated Holder-McCarthy inequality for positive operators and Ky Fan's inequality for real numbers are given as well.

TL;DR: The rank of a graph G is defined to be the rank of its adjacency matrix as mentioned in this paper, where the rank is defined as the sum of all the vertices of G with rank 5.

TL;DR: In this article, the existence of post-Lie algebra structures on pairs of Lie algebras (g, n ) defined on a fixed vector space V was studied, and it was shown that if there exists a post-lie algebra structure on ( g, n ), where g is nilpotent, then n must be solvable.

TL;DR: In this article, an algorithm using Grobner bases was proposed to decide in terms of the existence of a non singular matrix P if two Leibniz algebra structures over a finite dimensional C -vector space are representative of the same isomorphism class.

TL;DR: In this paper, it was shown that every Riordan array induces two characteristic combinatorial sums in three parameters n, k, m is an element of Z, and these parameters can he specialized and generate an indefinite number of other combinatorsial identities which are valid in the hi-infinite realm of recursive matrices.

TL;DR: In this paper, the Fiedler linearization is extended from square to rectangular matrix polynomials, and it is shown that minimal indices and bases of polynomial coefficients can be recovered from those of any linearization in this class via the same simple procedures developed previously for square coefficients.

TL;DR: In this article, the authors present sufficient conditions for a bipartite graph to be Hamiltonian and a graph to traceable, respectively, under the assumption that the graph is traceable.

TL;DR: In this paper, the authors presented a more general structure, namely the weighted directed graphs and provided appropriate generalizations of several existing results for mixed graphs related to singularity of the corresponding Laplacian matrix.

TL;DR: It is shown how the consensus in different types of network topologies is accelerated by considering not only nearest neighbors but also the influence of long-range interacting ones.