University of Wyoming Open Journals
Not a member yet
3193 research outputs found
Sort by
The numerical radius of a weighted shift operator
No full textIn this paper, the point spectrum of the real Hermitian part of a weighted shift operator with weight sequence a_1, a_2, . . . , a_n, 1, 1, . . . is investigated and the numerical radius of the weighted shift operator in terms of the weighted shift matrix with weights a_1, a_2, . . . , a_n is formulated explicitly
Rank drops of recurrence matrices
No full textA recurrence matrix is a matrix whose terms are sequential members of a linear homogeneous recurrence sequence of order k and whose dimensions are both greater than or equal to k. In this paper, the ranks of recurrence matrices are determined. In particular, it is shown that the rank of such a matrix differs from the previously found upper bound of k in only two situations: When (a_j) satisfies a recurrence relation of order less than k, and when the nth powers of distinct eigenvalues of (a_j ) coincide
Remarks on an operator Wielandt Inequality
No full textLet A be a positive operator on a Hilbert space H with 0 0, and Φ be a 2-positive unital linear map. Define Î = (Φ(X*AY )Φ(Y*AY )^(â1)Φ(Y*AX)^p Φ(X*AX)^(âp). Several upper bounds for (1/2) |Î + Î*| are established. These bounds complement a recent result on the operator Wielandt inequality
Spectral Properties of Finite-dimensional Waveguide Systems
No full textThis is a largely expository paper in which we study a finite dimensional model for gyroscopic/waveguiding systems. We study properties of the spectrum that play an important role when computing with such models. The notion of "waveguide type" is defined and explored in this context and Theorem 3.1 provides a form of the central result (due to Abramov) concerning the existence of real spectrum for such systems. The roles of semisimple/defective eigenvalues are discussed, as well as the roles played by eigenvalue "types" (or "Krein signatures"). The theory is illustrated with examples
Line segments on the boundary of the numerical ranges of some tridiagonal matrices
No full textTridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described
On the Main Eigenvalues of Universal Adjacency Matrices and U-Controllable Graphs
No full textA universal adjacency matrix U of a graph G is a linear combination of the 0â1 adjacency matrix A, the diagonal matrix of vertex degrees D, the identity matrix I and the matrix J each of whose entries is 1. A main eigenvalue of U is an eigenvalue having an eigenvector that is not orthogonal to the allâones vector. It is shown that the number of distinct main eigenvalues of U associated with a simple graph G is at most the number of orbits of any automorphism of G. The definition of a Uâcontrollable graph is given using controlâtheoretic techniques and several necessary and sufficient conditions for a graph to be Uâcontrollable are determined. It is then demonstrated that Uâcontrollable graphs are asymmetric and that the converse is false, showing that there exist both regular and nonâregular asymmetric graphs that are not Uâcontrollable for any universal adjacency matrix U. To aid in the discovery of these counterexamples, a gammaâLaplacian matrix L(gamma) is used, which is a simplified form of U. It is proved that any U-controllable graph is a L(gamma)âcontrollable graph for some parameter gamma
Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices
No full textIt is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible Hâmatrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with non-strictly diagonally dominant matrices and general Hâmatrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general Hâmatrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general Hâmatrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper
Preface special volume on the Conference on Graph Theory, Matrix Theory and Interactions
No full textRole Of Partial Transpose And Generalized Choi Maps In Quantum Dynamical Semigroups Involving Separable And Entangled States
No full textPower symmetric stochastic matrices introduced by R. Sinkhorn (1981) and their generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have been utilized to give positive block matrices with trace one possessing positive partial transpose, the so-called PPT states. Another method to construct such PPT states is given, it uses the form of a matrix unitarily equivalent to to its transpose obtained by S.R. Garcia and J.E. Tener (2012). Evolvement or suppression of separability or entanglement of various levels for a quantum dynamical semigroup of completely positive maps has been studied using Choi-Jamiolkowsky matrix of such maps and the famous Hordeckis criteria (1996). A Trichotomy Theorem has been proved, and examples have been given that depend mainly on generalized Choi maps and clearly distinguish the levels of entanglement breaking
Mean matrices and conditional negativity
No full textIn earlier papers R. Bhatia and H. Kosaki have shown that certain matrices associated with means are infinitely divisible. In this paper it is shown that many of them possess a stronger property: their Hadamard reciprocals have exactly one positive eigenvalue