In a distance-regular graph, the partition with respect to distance from a vertex supports a unique eigenvector for each eigenvalue. There may be non-singleton vertex sets whose corresponding distance partition also supports eigenvectors. We consider the members of three families of distance regular graphs, the Johnson Graphs, Hamming Graphs and Complete Multipartite graphs. For each we determi...

Quantum phase estimation algorithm finds the ground state energy, the lowest eigenvalue, of a quantum Hamiltonian more efficiently than its classical counterparts. Furthermore, with different settings, the algorithm has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate e...

We show that correlation matrices with particular average and variance of the coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for largest eigenvalue alignment corresponding eigenvector. explain how to which extent, distinctly large an approximately diagonal eigenvector generically occur specific independently matrix dimension.

We present a general framework for the a posteriori estimation and enhancement of error ineigenvalue/eigenvector computations for symmetric and elliptic eigenvalue problems, and provide detailedanalysis of a specific and important example within this framework—finite element methods with continuous,affine elements. A distinguishing feature of the proposed approach is that it provide...

We consider a conforming finite element approximation of the Reissner-Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are superconverg...

Let B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T is a linear operator on B which is positive and eventually compact, y is a positive vector, and A is a positive real. It is shown that (XI—TY1y is positive if, and only if, y is annihilated by the absolute value of any generalized eigenvector of T* associated with a strictly positive eigenvalue not less than...

In this note we prove lower bounds on the components of the eigenvector associated with the dominant eigenvalue of a graph. These bounds depend only on the eccentricity of the corresponding node and on the eigenvalue As corrollary lower bounds on the dominant eigenvalue are derived, which depend on the diameter of the graph. These bounds were motivated by a heuristic algorithm for finding perip...

An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero, and it is well known that a graph has exactly one main eigenvalue if and only if it is regular. In this work, all connected unicyclic graphs with exactly two main eigenvalues are determined. c © 2006 Elsevier Ltd. All rights reserved.

We study M-tensors and various properties of M-tensors are given. Specially, we show that the smallest real eigenvalue of M-tensor is positive corresponding to a nonnegative eigenvector. We propose an algorithm to find the smallest positive eigenvalue and then apply the property to study the positive definiteness of a multivariate form.