Showing papers in "Linear Algebra and its Applications in 2009"

TL;DR: A periodic consensus protocol for multi-agent systems with double-integrator dynamics is obtained and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains.

TL;DR: Wang et al. as mentioned in this paper established a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2 =C3.

TL;DR: In this article, the Laplacian-energy like invariant LEL (G) and the incidence energy IE (G ) of a bipartite graph are proposed, equal to the sum of the square roots of the eigenvalues, and the singular values of the incidence matrix of the graph G.

TL;DR: In this article, the optimal iteration parameters and the corresponding optimal semi-convergence factor for the parameterized Uzawa method were determined for solving singular saddle point problems under suitable restrictions on the involved iteration parameters.

TL;DR: In this article, the authors studied the problem of finding a (P, Q )-symmetric solution to a linear real quaternion matrix equation and provided necessary and sufficient conditions for the existence of a solution.

TL;DR: In this paper, lower bounds for μ 1 and upper bounds for ED(G) were obtained and the best possible upper bounds were derived for the D-spectral radius of a graph G. The D-energy of a given graph G is the sum of the absolute values of its D-eigenvalues.

TL;DR: In this article, the authors studied the Riemannian metric on the manifold of positive definite matrices, defined by a kernel function ϕ in the form K D ϕ (H, K ) = ∑ i, j ϕ( λ i, λ j ) - 1 Tr P i HP j K when ∑ √ i λ p i P i is the spectral decomposition of the foot point D and the Hermitian matrices H, K are tangent vectors.

TL;DR: In this paper, the 1-1 correspondence between equiangular frames of n vectors and graphs with n vertices was studied for R d graphs with more than 2 eigenvalues.

TL;DR: It is explained in this paper how to obtain numerically in the complex field the generic rank of tensors of arbitrary dimensions, based on Terracini’s lemma, and compare it with the algebraic results already known in the real or complex fields.

TL;DR: In this article, the authors investigate the interplay arising between max algebra, convexity and scaling problems, and describe such scalings by means of the max algebraic subeigenvectors and Kleene stars of nonnegative matrices.

TL;DR: In this paper, it was shown that only a fraction of 2 - Ω (n) of the graphs on n vertices have an integral spectrum, and no upper bound for their number has been known.

TL;DR: In this article, a fast random projection type approximation algorithm for the NNLS problem is presented, which employs a randomized Hadamard transform to construct a much smaller NLS problem and solves this smaller problem using a standard NLS solver.

TL;DR: In this paper, the concept of extremal biderivation of a triangular algebra is defined, and it is shown that under certain conditions, under certain assumptions, the extremal and inner biderivities of a triangle algebra can be combined.

TL;DR: In this article, it was shown that the singularities of a matrix-valued non-commutative rational function which is regular at zero coincide with the singularity of the resolvent in its minimal state space realization.

TL;DR: The (optimal) nonstationary extrapolation is introduced to improve the convergence rates of the well-known Modulus Algorithm and Block ModulusAlgorithm for its solution of the LCP.

TL;DR: In this paper, it was shown that the unitary Cayley graph X n is hyperenergetic if and only if n has at least two prime factors greater than 2 or at least three distinct prime factors.

TL;DR: In this article, three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have been introduced in the context of compressed sensing and studied for matrices that are Kronecker products.

TL;DR: In this paper, the Laplacian-like energy of a graph of order n has been studied and it is shown that the k-th coefficient c k is largest when the graph is a cycle C n and smallest when it is a S n with an additional edge between two of its pendent vertices.

TL;DR: In this paper, the problem of Kronecker invariants assignment by state feedback in singular linear systems is studied and resolved, and a generalization of the previous results of state feedback action on singular systems is presented.

TL;DR: In this article, the authors present a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group, based on basic notions of representation theory of finite groups.

TL;DR: Tan and Liu as discussed by the authors characterized the nullity set of unicyclic graphs with η (G ) = n - 5, and showed that if G is a unicycle graph, then η(G ) equals n − 2 ν (G) -1, n −2 ν(G) + 2, or n - 2 ξ (G + 2 ) + 2.

TL;DR: In this article, the inner product between any two frame vectors is always a common multiple of the cube roots of unity, which is equivalent to the existence of equiangular tight frames for complex Seidel matrices.

TL;DR: In this article, the authors consider the nonlinear matrix equation X = Q + ∑ i = 1 m M i X δ i M i ∗ where Q is positive definite and M i is arbitrary (resp. nonsingular) matrices.

TL;DR: In this article, the authors revisited the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system.

TL;DR: The nullity of a graph is defined to be the multiplicity of the eigenvalue zero in the spectrum of the adjacency matrix of the graph as mentioned in this paper, and the nullity set of bipartite graphs of order n is known.

TL;DR: In this paper, it was shown that if the von Neumann algebras A and B are type I factors, then a nonlinear bijective map Φ : A → B satisfies Φ( [ A, B ] ∗ ) = [ Φ ( A ), Φ ∈ A ) ∈ B if and only if Φ is a *-ring isomorphism.

TL;DR: In this paper, it was shown that the matrix algebra M n (B ), n ⩾ 2, where B is any unital algebra, is always zero product determined, and under some technical restrictions it is also zero Jordan product determined.

TL;DR: In this article, the authors considered the case where one of A, B, C has full column rank, and showed that Kruskal's uniqueness condition implies a recently obtained uniqueness condition.

TL;DR: In this article, the authors considered the set of m × n nonnegative real matrices and defined the nonnegative rank of a matrix A to be the minimum k such that A = BC where B is m × k and C is k × n.

TL;DR: In this paper, it was shown that if m⩾9 and G has no 4-cycle, then μ2⩽m, with equality if G is a star, fails for 4 ⩾m ⩽8.