Showing papers in "Linear Algebra and its Applications in 2022"

TL;DR: In this article , transposed Poisson algebra structures on block Lie algebras B(q) and block Lie superalgebrains S(q), where q is an arbitrary complex number, were described.

TL;DR: In this paper , it was shown that if G is a C5-free or C6-free graph of even size m ≥ 14 and G contains no isolated vertices, then ρ(G)≤ρ˜(m), with equality if and only if G≅Sm+42,2−, where ρ˜ (m) is the largest root of x4−mx2−(m−2)x+(m2−1)=0.

TL;DR: In this article , the transposed Poisson algebra structures on Witt type Lie algebras V(f), where f:Γ→C is non-trivial and f(0)=0.

TL;DR: A comprehensive categorization of block Gram-Schmidt algorithms, particularly those used in Krylov subspace methods to build orthonormal bases one block vector at a time, can be found in this paper .

TL;DR: In this paper , the existence of an odd [1, b]-factor in a graph G of even order n was shown to be provable in the presence of a spanning subgraph F of G with dF(x)∈{1,3,⋯,b} for every x∈V(G), where b is a positive odd integer.

TL;DR: In this paper , it was shown that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach space, which resolves the Tingley's problem.

TL;DR: In this paper, it was shown that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach space, which resolves the Tingley's problem.

TL;DR: In this article, the adjacency, Laplacian and incidence matrices for a quaternion unit gain graph were defined, and bounds for both the left and right eigenvalues of the adjACency matrix were derived for the cycle and path graphs.

TL;DR: In this article , an Extended Sparse Randomized Kaczmarz (ESK) method was proposed to solve the regularized basis pursuit problem and showed linear expected convergence to a sparse least square solution.

TL;DR: In this paper , the authors investigated geometric and topological properties of a generalization of classical majorization to positive weight vectors, and derived a new simplified characterization of $d$-majorization.

TL;DR: In this article, it was shown that the number of Laplacian eigenvalues in I in terms of structural parameters of G can be reduced to n − α (G ) and m G ( n − 1, n ] ≤ 1.

TL;DR: In this article , the algebraic structure of the rank two Racah algebra is studied in detail, and an automorphism group of this algebra is provided, which is isomorphic to the permutation group of five elements.

TL;DR: In this article , the density of free modules over a finite chain ring R of size qs is derived for linear codes over R. In particular, the density results can be bounded by the Andrews-Gordon identities.

TL;DR: In this article , the authors determined the graph having the maximum A α -spectral radius for α ∈ [ 1 2 , 1 ) among all connected graphs of size m and diameter d .

TL;DR: In this article , a non-abelian cohomology group Hnab2(gT,hS) is defined for Rota-Baxter Lie algebras.

TL;DR: In this paper , the root polynomials of a polynomial matrix P(λ) with coefficients in an arbitrary field were studied and the root vectors of a rational matrix R(λ, possibly singular and possibly with coalescent pole/zero pairs.

TL;DR: In this paper , the authors give a description of the images of polynomials with zero constant term on 3×3 upper triangular matrix algebras over an algebraically closed field.

TL;DR: In this article , it was shown that for any tree T with n vertices, E φ (T ) ≥ 2 n − 1 φ 1 , (n − 1 ) , with equality holding if and only if T ≅ S n .

TL;DR: In this paper , the block Macaulay matrix is used to solve multidimensional multiparameter eigenvalue problems (MEPs), where the data in the column space of the sparse and structured block matrix is considered directly, avoiding the computation of a numerical basis matrix of the null space.

TL;DR: In this article , a geometric perspective on the fact that the effective resistance is a metric on the nodes of a graph is discussed, and a matrix identity of Miroslav Fiedler is presented.

TL;DR: In this article , a necessary and sufficient condition on the Laplacian spectral radius of hypergraphs such that the complement of that hypergraph is connected is given, and some upper bounds of the Nordhaus-Gaddum type are obtained for the sum of the spectral radius for a k-uniform hypegraph and its complement.

TL;DR: In this article , the explicit value of the quadratic embedding constants of the path graphs was derived for a family of matrices, and the positive definiteness of these matrices was characterized.

TL;DR: The Hafnian Master Theorem as discussed by the authors is a generalization of the classical Permanent Master theorem of MacMahon, and it provides an easy-to-compute generating function for the hafnians related to a remarkable class of multivariate random variables whose sampling and probability density function are ♯P-hard for computing.

TL;DR: In this article , it was shown that P-independent sets are those given by right linearly independent sets when partitioned into conjugacy classes and that finitely generated P-closed sets correspond to lists of finite-dimensional right vector spaces.

TL;DR: In this paper , a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras is provided.

TL;DR: In this paper , the authors characterized the exceptional (p, q)-sums for polynomials with degree 2 over an arbitrary field F, where at least one polynomial p and q is irreducible over F.

TL;DR: In this article , the A-spectral radius of n×n operator matrices with entries are commuting A-bounded operators, where A=diag(A,A,…,A) is an n× n diagonal operator matrix.

TL;DR: In this article , the eigenvalue multiplicity of unicyclic graphs was investigated and the main conclusion of Wong, Zhou and Tian (2020) was improved by Wu et al. They showed that k ≥ n−43 and all extremal graphs attaining the upper bound are characterized.

TL;DR: In this paper , the authors provide a complete parametric characterization of all complex, real and rational orthogonal permutative matrices of order $4.$ and show that any such matrix can always be expressed as a linear combination of up to four permutation matrices.

TL;DR: In this article , a generalization of the classical Skjelbred-Sund method, used to classify nilpotent low-dimensional Lie algebras, in order to classify Lie-Yamaguti algesbras with non-trivial annihilator was proposed.