Showing papers in "Linear Algebra and its Applications in 2018"

TL;DR: It is shown that, in this scenario, classical perturbation results, such as Weyl and Davis-Kahan, can be improved significantly and many of the new bounds are close to optimal and also discuss some applications.

TL;DR: In this article, the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space was investigated, and it was shown that these sets are convex for d ≥ 2.

TL;DR: In this article, a family of linear sets of PG (1, q 2 n ) arising from maximum scattered linear sets (3, q n ) of pseudoregulus type was introduced.

TL;DR: This paper proposes a homogeneous formula for the definition of P- and P0-tensor classes, and shows that many checkable classes of structured tensors, such as the nonsingular M-tensors, the nonsedular H-Tensors with positive diagonal entries, the strictly diagonally dominant tensors with Positive semi-definite entries, are P-tENSors under the new definition, regardless of whether the order is even or odd.

TL;DR: In this article, the spectral radius ρ α (G ) of a graph with adjacency matrix A (G) was shown to be ρ 1 / 2 (G ), with equality holding if and only if G = B n − k + 2, ⌊ k / 2 ⌋, ⌈ k/ 2

TL;DR: In this paper, the extremal tree with maximal A α -spectral radius with fixed order and cut vertices is characterized, which generalizes some known results, including the conjecture of Nikiforov and Rojo.

TL;DR: In this article, three edge graft transformations on the A α -spectral radius of a graph have been proposed to determine the unique graph with the maximum A α-Spectral radius among all connected graphs with diameter d.

TL;DR: An exact closed-form formula is conducted for the mean squared error of the iterate generated by the randomized Kaczmarz method, which completes the existing closed- form formula derived only for the tall coefficient matrix.

TL;DR: In this paper, a correspondence between one-generator braces and indecomposable, non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation is established.

TL;DR: In this paper, the A α -spectrum of a graph G is defined to be the root of all roots of A α-characteristic polynomials of G. And then, it is shown that the Aα -spectra are much more efficient for us to distinguish graphs.

TL;DR: A priori accuracy estimates for low-rank matrix approximations that use just a small number of the rows and columns are proposed, which are more accurate than previously known ones.

TL;DR: In this article, the energy of the general extended adjacency matrix A = (a i j ) of a simple graph of order n and size m is defined as a i j = F (d i, d j ) if the vertices v i and v j are adjacent, and a I j = 0 otherwise.

TL;DR: A definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices, is introduced and three promising applications of such submatrices are presented.

TL;DR: The theory of equiangular lines in Euclidean spaces has been studied in this paper, where it is shown that the cardinality of a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class.

TL;DR: This paper gives some results on the eigenvalues of $A_{\alpha}(G)$ with $\alpha>1/2$ and proves that the extremal graphs with equality holding have $\lambda_k(A_{ \alpha} (G)))\leq\alpha n-1$ for $2\Leq k\lequ n$.

TL;DR: In this article, a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form C ˜ ( ∑ k = 1 K h k ( s ) A ˜ k ) − 1 B ǫ where h 1, h 2,..., h K are prescribed functions that specify the surmised structure of the model.

TL;DR: In this article, some new results for the ABC eigenvalues and the ABC energy of a graph are presented, which are related closely to the atom-bond connectivity (abbreviated as ABC) index.

TL;DR: In this article, the biderivations of the block Lie algebras B ( q ) for all q ∈ C were determined, and it was shown that the space of bidersivations is spanned by inner bidersions and one outer biderivation.

TL;DR: In this paper, the first two largest spectral radii among all supertrees in S (m, d, k ) were determined for 3 ≤ d ≤ m − 1, where d is the diameter of the supertree.

TL;DR: In this paper, it was shown that the length of a generating set of n × n matrices over the field F cannot exceed 2 n − 2 if the generating set S contains a nonderogatory matrix.

TL;DR: In this paper, it was shown that η ≤ Δ − 1 Δ n for an arbitrary graph G with order n and maximum degree Δ, and the equality holds if and only if G is the disjoint union of some copies of K Δ, Δ.

TL;DR: The tensor rank of tensor product of two three-qubit W states is not less than eight as discussed by the authors, which is the upper bound of the tensor ranking of many three-quantity W states.

TL;DR: In this article, the authors study the Brown measure of certain non-Hermitian operators arising from Voiculescu's free probability theory, and show that these operators appear as the limit in ⋆-moments of certain ensembles of random matrices and give then a canonical candidate for the limit eigenvalue distribution.

TL;DR: It is shown that if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t is not multiplicative under taking a sufficiently hight tensor product power.

TL;DR: In this article, it was shown that for every n × n matrix A over the field Z 2 there exists an idempotent matrix E such that (A − E ) 4 = 0.

TL;DR: For a simple graph G of order n, size m and with signless Laplacian eigenvalues q 1, q 2, q 3, q 4, q 5, q 6, q 7, q 8, q 9, q 10, q 11, q 12, q 13, q 14, q 15, q 16, q 17, q 18, q 19, q 20, q 21, q 22, q 23, q 24, q 25, q 26, q 27, q 28, q 29, q 30, q 31,

TL;DR: A survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented in this paper, where a preference for the procedure of the author is exhibited for the test problems.

TL;DR: In this article, a combinatorial characterization of the coefficients of the characteristic polynomials of oriented hypergraph Laplacian and adjacency matrices via a signed hypergraph generalization of basic figures of graphs is presented.

TL;DR: This paper revisits the classical problem of finding the best rank-1 approximation to a generic tensor and proposes a simple tactic to partially close the gap between conventional and SVD algorithms.

TL;DR: In this article, the unique hypertrees with maximum spectral radius among k-uniform non-hyper-caterpillars with m edges and diameter d for 4 ≤ d ≤ m − 2, for m ≥ 6, and for 0 ≤ s ≤ ⌊ m − 1 2 2 ⌋, respectively.