Showing papers in "Linear Algebra and its Applications in 2015"

TL;DR: This paper defines a new tensor–tensor product alternative to the t-product and generalizes the transform-based approach to any invertible linear transform, and introduces the algebraic structures induced by each new multiplication in the family, which is that of C⁎-algebras and modules.

TL;DR: The Hermitian-adjacency matrix as mentioned in this paper is a complex adjacency matrix of a mixed graph, which is a Hermitians matrix and called the Hermitia-Adjacency Matrix.

TL;DR: This work addresses the numerical problem of recovering large matrices of low rank when most of the entries are unknown by exploiting the geometry of the low-rank constraint to recast the problem as an unconstrained optimization problem on a single Grassmann manifold and applies second-order Riemannian trust-region methods and preconditioned methods to solve it.

TL;DR: In this article, two block versions of the Kaczmarz method with a randomized projection, designed to converge in expectation to the least squares solution, are presented. But neither of these methods can guarantee linear convergence when the matrix has consistent row norms and when the row norms are unbounded.

TL;DR: This work studies estimation of M-matrices taking the role of inverse second moment or precision matrices using sign-constrained log-determinant divergence minimization, and proposes an algorithm based on block coordinate descent in which each sub-problem can be recast as non-negative least squares problem.

TL;DR: In this article, it was shown that the problem of computing the zero forcing number of a directed graph allowing loops is also NP-hard, and a necessary and sufficient condition in terms of zero forcing sets for the strong controllability of a system with a tree-structure was given.

TL;DR: Some properties of their tensor counterparts are established: strong H -tensors and (general) H -Tensors.

TL;DR: In this paper, a numerical radius inequality for general n × n operator matrices is given, which improves a well-known inequality of J.C. Hou and H.K. Du.

TL;DR: In this paper, it was shown that the largest Laplacian H-eigen-value of a k-uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even.

TL;DR: In this paper, the authors considered the problem of representing a continuous-time quantum walk in a graph X by the matrix exp ⁡ ( − i t A ( X ) ) and provided necessary and sufficient criteria for distance-regular graphs to have perfect state transfer.

TL;DR: In this paper, the adjacency or signless Laplacian spectral radius of a simple graph G is characterized for all non-odd-bipartite hypergraphs G k, k 2 of fixed order.

TL;DR: The relation between the Laplacian characteristic polynomial of a signed graph and adjacency polynomials of its signed line graph and signed subdivision graph was established in this paper.

TL;DR: In this article, the authors develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker tensors, an efficient structured tensor format based on recursive subspace factorizations.

TL;DR: In this article, the authors discuss Mobius transformations for general matrix polynomials over arbitrary fields, analyzing their influence on regularity, rank, determinant, and structural features including sparsity and symmetry.

TL;DR: A complete direct solution in a compact vector form is obtained to an unconstrained optimization problem to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition.

TL;DR: In this article, the Cartesian decomposition of T ∈ B (H) is shown to be a Cartesian operator decomposition, and a refinement of the triangle inequality is also shown.

TL;DR: In this paper, it was shown that every 2-local derivation on a finite-dimensional semi-simple Lie algebra over an algebraically closed field of characteristic zero is a derivation.

TL;DR: In this paper, the authors give sufficient conditions such that the recursive matrix A is totally positive, where A = [ a n, k ] n, k ≥ 0 is an infinite lower triangular matrix defined by the recurrence a 0, 0 = 1, a n + 1, k = r k a n, s k, t k, t k are all nonnegative.

TL;DR: In this paper, the authors generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space, and establish some numerical radius inequalities for A α X B α and Aα X B 1 − α ( 0 ≤ α ≤ 1 ) and Heinz means under mild conditions.

TL;DR: The proposed methods, based on standard versions of ordinary differential equations, in the matrix setting, are a more practical alternative for large-scale problems arising in applications and make the application of higher order methods feasible.

TL;DR: For all n ≥ 3, there exist n − 1 threshold graphs of order n 2, pairwise noncospectral, each equienergetic to K n 2 as mentioned in this paper.

TL;DR: In this article, a tensor eigenvalue inclusion set for weakly irreducible tensors was given, which proved to be tighter than those in L.Q. Qi (2005) and C.T. Kong (2014).

TL;DR: In this paper, it was shown how to transform Toeplitz matrix structures into Cauchy matrix structures using the Fast Multipole Method (FMM) and then combine the same transformation with a link to the Hierarchical Semiseparable matrix structure.

TL;DR: In this paper, the spectral characterization problem of signed lollipop graphs was extended to the adjacency matrix and Laplacian matrix of the signed graphs, and it was shown that the spectral properties of a signed lipop graph can be determined by the spectrum of its LaplACian matrix.

TL;DR: In this article, a lower bound for the Laplacian energy of a simple graph with n vertices, m edges, maximum degree Δ, average degree d = 2 m n, clique number ω has been obtained.

TL;DR: Two new classes of tensors are proposed: double B-tensors and quasi-double B-Tensors, and it is shown that even order symmetric double B -tensor and even order asymmetric quasi-Double B- tensors are positive definite.

TL;DR: In this paper, Wu et al. gave sufficient conditions on the spectral radius for a bipartite graph being Hamiltonian and traceable, which improved the results of Yu and Fan.

TL;DR: The Z-eigenpair of a tensor, in particular, an irreducible nonnegative tensor is considered and some bounds for the eigenvector and Z-spectral radius are presented.

TL;DR: In this article, it was shown that for a simple graph G, η (G ) ≤ | V ( G ) | − 2 m (G) + 2 c (G ), where c(G ) is the number of connected components of G.

TL;DR: In this article, it was shown that if a ≠ − b, then a two-distance set that forms a tight frame for R n is a spherical embedding of a strongly regular graph.