We use the QR-decomposition to obtain the eigenvalues of a matrix. The method is iterative and builds an upper-triangular matrix. The eigenvalues appear as the diagonal terms of this upper-triangular matrix. These values are found to be in agreement with those given by the Mathematica built-...
The fundamental solution for the Brownian motion of the eigenvalues of a random matrix in Dyson's (1) model is represented as an integral with respect to the measure on the orthogonal group in N dimensions. The solution is discussed for some special cases only. In two dimensions the distribut...
Siam Journal on Matrix Analysis & ApplicationsM. T. Chu, "Constructing a Hermitian matrix from its diagonal entries and eigenvalues," SIAM J. Matrix ... MT Chu - 《Siam Journal on Matrix Analysis & Applications》 被引量: 80发表: 1995年 Eigenfunctions of composite Hermitian operators with appl...
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space #36;l^2(#92;mathbb{N})#36; by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator...
Eigenvalues, diameter, and mean distance in graphs It is well-known that the second smallest eigenvalue λ 2 of the difference Laplacian matrix of a graph G is related to the expansion properties of G. A more detailed analysis of this relation is given. Upper and lower bounds on the ......
Sojourn Times and Asymptotic Properties of the Scattering Matrix It is shown that generalized gradient approximations (GGAs) for exchange only, due to their very limited form, quite generally can not simultaneously repro... GUILLEMIN,V. - 《Publications of the Research Institute for Mathematical Scie...
to two distinct Hecke eigenforms supported at positive integers represented by a primitive integral binary quadratic form with negative discriminant whose class number is 1. We provide a quantitative result for the number of sign changes of such sequence in the interval(x,2x]for sufficiently large....
Krause, “Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix,” Linear Algebra and Its Applications, vol. 142, pp. 195–209, 1990. CrossRef N. Gozlan, “A characterization of dimension free concentration in terms of transportation inequalities,” The ...
matrix) + "}" stiffness_matrix_str = numpy_to_mathematica(stiffness_matrix) mass_matrix_str = numpy_to_mathematica(mass_matrix) # Start a Wolfram Language session session = WolframLanguageSession() # Wolfram code to calculate eigenvalues and eigenvectors wolfram_code = f""" stiffnessMatrix = ...
equation of the closed loop system, and compare it with a direct computation of eigenvalues of a symplectic hamiltonian matrix arising from a finite ... A Manitius,H Tran - IEEE Conference on Decision & Control 被引量: 14发表: 1983年 Upper and lower bounds for the Schrödinger-equation ...