Showing papers in "Linear Algebra and its Applications in 2021"

TL;DR: In this article, the authors introduce different connectivity matrices and study their eigenvalues to explore various structural properties of a general hypergraph, including the diameter, connectivity and vertex chromatic number of a hypergraph.

TL;DR: For a positive even integer n ≥ 8 or n = 4, if G is an n-vertex graph with ρ ( G ) > θ ( n ), then G has a perfect matching.

TL;DR: It is shown that CSSP, the column subset selection problem, is NP-complete.

TL;DR: While for general unstructured differential-algebraic systems the characterization of these distances are partially open problems, it is shown that for dissipative Hamiltonian systems and related matrix polynomials there exist explicit characterizations that can be implemented numerically.

TL;DR: In this paper, the spectral study of weighted adjacency matrices of graphs weighted by some topological indices has been studied and the extremal trees with the largest radius of A f when f ( x, y ) is increasing and convex in variable x have been found.

TL;DR: Hoffman's ratio bound as mentioned in this paper is an upper bound for the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix of the graph.

TL;DR: In this article, the T-eigenvalues of third-order tensors are studied and a commutative tensor family is proposed, including Hermitian tensors.

TL;DR: In this paper, the numerical radius of a bounded linear operator on a complex Hilbert space was shown to be upper bounded by a circular disk with center at the origin and radius 1 2.

TL;DR: In this article, it was shown that S n, k is the unique graph attaining the maximum signless Laplacian spectral radius among all graphs of order n containing no F k, provided that k ≥ 2 and n ≥ 3 k 2 − k − 2.

TL;DR: It is proved that the square root of Jensen-R\'enyi divergences is a distance metric and a proof of the metric property of the Quantum Jensen-Shannon divergence is obtained.

TL;DR: In this article, it was shown that each non-smooth 2-dimensional Banach space has the Mazur-Ulam property, where the unit ball has a unique supporting functional at each point of the unit sphere.

TL;DR: The first-known error bound on the linear approximation of the truncated singular value decomposition of a perturbed rank-$r$ matrix is introduced and it is shown that this bound holds universally for perturbations with arbitrary magnitude.

TL;DR: In this paper, the authors give a complete description of the image of polynomials with zero constant term on 2 × 2 upper triangular matrix algebras over an algebraically closed field.

TL;DR: In this paper, it was shown that if the A α -spectral radius of a graph G is not less than the largest root of x 3 − ( ( α + 1 ) n + α − 4 ) x 2 + ( α n 2 + α 2 − 2 α − 1 ) x − α 2 n 2+ ( 5 α 2−3 α + 2 ) n − 10 α 2 + 15 α − 8 = 0 then G has a perfect matching unless G = K 1 ∇ ( K n − 3 ∪ 2 K 1 ).

TL;DR: In this paper, an extension of the classical numerical radius based on the Birkhoff-James orthogonality was introduced, called the w N (T ), where T ∈ B (H) is the identity operator.

TL;DR: In this article, convolutional proximal neural networks (cPNNs) are proposed for denoising signals and images, where the achieved quality depends on the Lipschitz constant.

TL;DR: In this paper, the authors considered the natural follow-up to the randomized control scheme, greedy strategies like the greedy probability criterion and the almost-maximal residual control, and showed convergence to a least-squares least-norm solution.

TL;DR: In this article, it was shown constructively that under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method.

TL;DR: In this paper, it was shown that any pair of column subspaces corresponding to two different clusters are nearly orthogonal: the minimal principal angle between them is at most π 2 − c 1 N θ − c 2 N h, for some constants c 1, c 2 depending only on the multiplicities of the clusters.

TL;DR: The first main topic is the development of error bounds regarding the approximated output vector within the time limits and strategies that enable an efficient numerical execution of time-limited balanced truncation for large-scale systems are proposed.

TL;DR: In this article, the authors give several refined and generalized numerical radius inequalities for 2 × 2 operator matrices, which improve and generalize earlier related inequalities, and an application of some of their results is also given.

TL;DR: In this article, it was shown that under the action of GL ( 2, q 6 ) there are ( q 2 + q + 1 ) ( q − 2 ) / 2 ⌋ equivalence classes of maximum scattered subspaces of the form U b = { ( x, b x q + x q 4 ) : x ∈ F q 6 } in F q 2 × F q 4.

TL;DR: An exact closed-form formula is conducted for the mean-squared residual of the iterate generated by the randomized Gauss-Seidel method, and an upper bound for the convergence rate of the randomizedGauss- Seidel method is estimated.

TL;DR: In this paper, the spectral radius of the Reciprocal distance matrix, the reciprocal distance Laplacian matrix, and the RDL signless matrix was studied. But the spectral distance matrix is not a regular matrix.

TL;DR: In this article, the authors describe two methods, both inspired from Godsil-McKay switching on simple graphs, to build cospectral gain graphs whose gain group consists of the complex numbers of modulus 1 (the circle group).

TL;DR: In this paper, the authors determined the unique graph with maximum α-index among all graphs of order n with no 4-cycle and 5-cycle, respectively, and partially answer a proposed problem in Nikiforov (2017).

TL;DR: In this article, the authors define the f-weighted Laplacian matrix for random graphs in the Erdos-Renyi random graph model G n, p, where p ∈ ( 0, 1 ) is fixed.

TL;DR: In this article, a new class of non-singular H-matrices, called CKV-type matrices, is proposed, which is called CK-SDD class.

TL;DR: In this paper, a simple method to test if a given matrix is copositive by solving a single mixed-integer linear programming (MILP) problem is described, which requires no special coding to implement and takes advantage of the computational power of modern MILP solvers.