Showing papers in "Linear Algebra and its Applications in 2017"

TL;DR: In this paper, an iterative hard thresholding algorithm was proposed for low-rank tensor matrix recovery from a small number of linear measurements, which is based on a variant of the restricted isometry property of the measurement operator adapted to the tensor decomposition at hand.

TL;DR: In this paper, a tensor-based representation of the connectivity hypermatrix of a general hypergraph is proposed. But the authors only consider the case of uniform hypergraphs and do not consider the spectral properties of these hypermatrices.

TL;DR: In this article, it was shown that the spectral radius of a tree of maximal degree Δ satisfies the tight inequality ρ ( A α ( T Δ ) ) α Δ + 2 ( 1 − α ) Δ − 1, which implies previous bounds of Godsil, Lovasz, and Stevanovic.

TL;DR: This work finds new mild deterministic conditions for the uniqueness of individual rank-$1$ tensors in CPD and presents an algorithm to recover them, which is algebraic because it relies only on standard linear algebra.

TL;DR: This paper presents two complex Zhang neural network models with the Li activation function for computing the Drazin inverse of a complex time-varying square matrix and proves that the ZNN models globally converge in finite time.

TL;DR: In this article, the authors proposed an algorithm for approximating the logarithm of the determinant of a symmetric positive definite (SPD) matrix. But the algorithm is randomized and approximates the traces of a small number of matrix powers of a specially constructed matrix, using the method of Avron and Toledo.

TL;DR: In this paper, a new interesting property of linear time-delay systems was emphasized and a multiplicity induced stability criteria for reduced order systems; scalar delay-equations and a special class of second order systems.

TL;DR: This paper determines the unique k -uniform supertree with the maximum spectral radius among all k - uniform supertrees with a given degree sequence by using 2-switch operation and edge-moving operation on superTrees.

TL;DR: In this paper, it was shown that if G is d-regular then α 0 = − λ min ( A ( G ) ) d − (1 − α ) A( G ), where α 0 is the smallest α for which A α (G ) is positive semidefinite.

TL;DR: In this paper, the authors classify three dimensional evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

TL;DR: In this article, the generalized diffusion equation using the Laplace and factorial-transformed k-path Laplacian operators was shown to be self-adjoint and to produce super-diffusive processes when 1 < s < 3.

TL;DR: For Hankel matrices, this paper showed that total nonnegativity (resp. total positivity) of order r is preserved by sum, Hadamard product, and hadamard power with real exponent t ≥ r − 2.

TL;DR: This work gives an algebraic construction of new families of d -dimensional permutation-invariant codes on at least ( 2 t + 1 ) 2 ( d − 1 ) qudits that can also correct t errors for d ≥ 2 and proves constructively that an uncountable number of such codes exist.

TL;DR: In this paper, the authors investigate connections between the symmetries (automorphisms) of a graph and its spectral properties, and show that the techniques used to equitably decompose a graph can be used to bound the number of simple eigenvalues of undirected graphs, where they obtain sharp results of Petersdorf-Schmidt type.

TL;DR: This work presents an approach that incorporates a discrete values prior into basis pursuit, and shows that phase transition takes place earlier than when using the classical basis pursuit approach, and that, independently of the sparsity of the signal, measurements are necessary to recover a unipolar binary, and a bipolar ternary signal uniquely, where N is the dimension of the ambient space.

TL;DR: The spectra of uniform hypertrees are studied by using the generalized weighted incident matrix to show that λ is a nonzero eigenvalue of the hypertree H corresponding to an eigenvector with all elements nonzero if and only if κ is a root of the polynomial φ.

TL;DR: In this article, the authors consider the filtration of OqOq whose nth component is spanned by the products of at most n generators and show that the associated graded algebra is isomorphic to Uq+.

TL;DR: In this article, the authors investigated the H-rank of mixed graphs further, determining the Hranks of those mixed graphs with trees, cycles and complete bipartite graphs as underlying graphs, respectively.

TL;DR: In this paper, it was shown that if A and B are operators in B (H ) then w ( [ A B 0 0 ] ) ≤ 1 2 ( ‖ A ‖ + B B ⁎ + 1 2 ) for all t ∈ [ 0, 1 ], where w ( ⋅ ) and w (⋅ ǫ) denote the numerical radius and the usual operator norm, respectively.

TL;DR: In this article, it was shown that every surjective complex linear or conjugate linear isometry between the unit spheres of two trace class spaces admits a unique extension to a Surjective Complex Linear or Conjunctive Linear Isometry (SCLI) between the spaces.

TL;DR: For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, it is proved that the spectral norm remains invariant under specific subsets of unfolding operations.

TL;DR: In this article, the relation between the Kemeny constant and the effective graph resistance for a general connected, undirected graph has been established based on the Moore-Penrose pseudo-inverse of the Laplacian matrix.

TL;DR: In this paper, the spectral properties of super corona matrices and super neighbourhood corona matrix have been studied and all the eigenvalues and corresponding eigenvectors of these matrices have been described.

TL;DR: In this article, the authors characterized r-left symmetric (left asymmetric) and r-right asymmetric (right symmetric) operators in B (H ), where H is a real or complex Hilbert space.

TL;DR: A class of completely positive matrices with quadratic (in terms of the matrix size) completely positive rank, but with linear completely positive semidefinite rank is exhibited, and a connection to the existence of Hadamard matrices is made.

TL;DR: In this paper, the sign properties of Metzler matrices are investigated and sufficient conditions for the existence of common Lyapunov functions for all the matrices in the convex hull of a family of matrices containing both sign-and real-type entries are derived.

TL;DR: In this paper, an approximate orthogonality relation related to the Birkhoff norm was studied in the context of linear bounded operators on a Hilbert space, and the authors gave some properties of this relation as well as applications.

TL;DR: This paper introduces the block monotonicity and block-wise dominance relation for continuous-time Markov chains, and provides some fundamental results on the two notions, and shows that the stationary distribution vectors obtained by the block-augmented truncation converge to the stationary Distribution vector of the original BMMC.

TL;DR: In this article, two Brauer-type eigenvalue inclusion sets and some bounds on the spectral radius of uniform hypergraphs are given. But these bounds are not applicable to the case of tensors.

TL;DR: A condition number that admits a closed expression as the inverse of a particular singular value of Terracini's matrix, which represents the tangent space to the set of tensors of fixed rank is presented and a practical algorithm for computing this condition number is presented.