A Unified Extension of Some Results of Thompson, Marcus and Moyls.
A variance analog of majorization and some associated inequalities.
Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices
An eigenvalue inequality and spectrum localization for complex matrices.
An extension of a result of Lewis.
AnS-type upper bound for the largest singular value of nonnegative rectangular tensors
An S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.
Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
Bound for the largest singular value of nonnegative rectangular tensors
In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math. China, 2011, 6, 363-378.
Bounds and inequalities for the Perron root of a nonnegative matrix. III: Bounds dependent on simple paths and circuits.
Bounds for index of a modified graph
If a graph is connected then the largest eigenvalue (i.e., index) generally changes (decreases or increases) if some local modifications are performed. In this paper two types of modifications are considered: (i) for a fixed vertex, t edges incident with it are deleted, while s new edges incident with it are inserted; (ii) for two non-adjacent vertices, t edges incident with one vertex are deleted, while s new edges incident with the other vertex are inserted. ...
Bounds for sine and cosine via eigenvalue estimation
Define n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the first super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the first super- and subdiagonal are minus one. Then, denoting by λ(·) the largest eigenvalue, [...] Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain...
Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix.
Bounds for the singular values of a matrix involving its sparsity pattern.
Bounds for the spectral radius of block -matrices.
Bounds for the spectral radius of nonnegative matrices
Bounds for the Z-eigenpair of general nonnegative tensors
In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.
Bounds of modulus of eigenvalues based on Stein equation
This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
Bounds of the matrix eigenvalues and its exponential by Lyapunov equation
We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also...
Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices.
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...