Showing papers in "Linear Algebra and its Applications in 2019"

TL;DR: In this article, the authors prove upper and lower bounds for the A-numerical radius of a positive bounded operator in semi-Hilbertian spaces. But they do not consider the case where the operator T is a distinguished A-adjoint operator of A. In particular, they show that w A (T ) ≤ w A(T ), where | cos ⁡ | denotes the A cosine of angle of T.

TL;DR: In this article, the authors prove the inclusion of their spectra σ (B ) ⊆ σ(M ), and the equality of their spectral radii ρ ( B ) = ρ( M ) if M is nonnegative.

TL;DR: In this paper, the spectral radius of a bounded linear operator defined on complex Hilbert space has been shown to be upper and lower bounds for the number of zeros of a given polynomial.

TL;DR: When the coefficient matrix is assumed to be of full column rank, it is proved the convergence and derive an upper bound for the expected convergence rate of the partially randomized extended Kaczmarz method.

TL;DR: In this paper, the authors define a norm on the space of bounded linear operators on a Hilbert space, which generalizes the numerical radius norm, and investigate basic properties of this norm and prove inequalities involving it.

TL;DR: In this article, the convex combination of convex combinations D α (G ) of D i a g ( T r ) and D ( G ) is studied and the spectral properties of D α(G ) are given and a few open problems are discussed.

TL;DR: In this article, the authors presented a characterization of the connected simple Cayley graph Γ = Cay (G, S ) having perfect state transfer, where G is an abelian group and S is a non-empty set of G.

TL;DR: In this article, a weaker version of Nikiforov's conjecture is considered, and it is shown that for a given integer k ≥ 2, any graph G of sufficiently large order n with spectral radius μ (G) ≥ μ (S n, k ) (or μ ( G ) ≥ μ(S n, k + ) ≥ ρ (S N, k + ), unless G = S n, K (or G = ρ, k+ ).

TL;DR: In this paper, a spectral analysis of the adaptive local iterative filtering (ALIF) iteration matrices is presented, with a special attention to the eigenvalue clustering and eigen value distribution.

TL;DR: In this article, it was shown that if X is a two-dimensional real normed space such that its unit sphere contains a line segment with the distance between its endpoints being greater than 1, then X has the Mazur-Ulam property.

TL;DR: In this paper, a lower bound of λ 2 (A α (G ) ) for 0 ≤ α 1 was given, and it was shown that the star is the unique graph which minimizes the second largest A α -eigenvalues among connected graphs.

TL;DR: In this paper, the adjacency and Laplacian eigenvalues for some families of oriented hypergraphs are determined, which are analogous to cycles and paths in graphs and signed graphs.

TL;DR: In this article, the GM-switching method with cospectral complements is used to construct non-isomorphic non-convex non-co-occurrence graphs.

TL;DR: In this paper, a necessary and sufficient condition for the integrality of Cayley graphs over the dicyclic group T 4 n was given. And for a prime p, all integral Cayley graph families over T 4 p were determined.

TL;DR: In this paper, an upper bound for the infinity norm for the inverse of Dashnic-Zusmanovich type matrices is given, and it is proved that the upper bound is sharper than the well-known Varah's bound for strictly diagonally dominant matrices.

TL;DR: In this paper, the authors describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra, and describe the properties of these images.

TL;DR: In this article, the largest eigenvalue (called the index and denoted λ 1 ) of a signed graph has been shown to be upper bound λ 2 2 ≤ max ⁡ { d i m i − n i : 1 ≤ i ≤ n }, where d i is the vertex degree of i, m i = 1 d i ∑ j ∼ i d j and n i = ∑j ∼ i ( | N i σ ( i j ) ∩ N j σ( i j) ∩ n j − σ

TL;DR: It is proved that an analogous “universal” problem in the theory of tensors of order at most 3 over an arbitrary field is the problem of classifying three-dimensional arrays up to equivalence transformations.

TL;DR: In this article, majorization inequalities for different means of positive definite matrices were proved for Cartan mean, Karcher mean, Wasserstein mean, and power mean, respectively.

TL;DR: This paper studies some invariants of MRD codes and evaluates their value for the known families, providing a new characterization of generalized twisted Gabidulin codes.

TL;DR: This paper proposes a very efficient fast projected gradient method to tackle the problem in variables ( S, U, B ) and generate locally optimal solutions and shows the effectiveness of the proposed method compared to other approaches.

TL;DR: In this article, the generalized distance matrix of a simple connected graph G is defined as a convex combination of the convex combinations of T r (G ) + (1 − α ) D (G) for 0 ≤ α ≤ 1.

TL;DR: In this paper, it was shown that if both d (t ) and h(t ) are Polya frequency formal power series, then R is totally positive, i.e.

TL;DR: A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed, designed to succeed in situations where the standard rank-restricted isometry property fails, e.g. in case of subexponential unstructured measurements.

TL;DR: In this article, the authors proved that the projective eigenvariety admits a module structure, which is determined by the support of the tensor and can be characterized explicitly by the Smith normal form of the incidence matrix.

TL;DR: In this article, the authors characterized the digraph which has the maximal A α spectral radius in G n r, and also determined the unique digraph that attains the maximum (resp. minimum) Aα spectral radius among all strongly connected bicyclic digraphs.

TL;DR: Aguilar, Lee, Piato, and Schweitzer as mentioned in this paper showed that threshold graphs have no non-trivial eigenvalues in the interval [ − 1 − 2 ) / 2, ( − 1 + 2 )/ 2 ].

TL;DR: In this article, it was shown that for any tree T of order n ≥ 3, 2 cos ⁡ π n + 1 ≤ ρ ( Ω ( T ) ) ≤ n − 2, with equality in the left (resp., right) inequality if and only if T is isomorphic to the path P n (resp. the star K 1, n − 1 ).

TL;DR: In this article, the polynomial part of a rational matrix is expressed in a basis that satisfies a three-term recurrence relation, and a new family of strong linearizations of rational matrices is presented.

TL;DR: In this paper, the Riordan matrices were used to introduce the notion of a Riordan graph, which is a generalization of Pascal graphs and Toeplitz graphs, and also some other families of graphs.