Showing papers on "Spectrum of a matrix published in 1968"
TL;DR: In this article, a hermitian dynamical matrix in terms of Cartesian displacement coordinates is derived starting from a harmonic force constant matrix expressed using the Wilson's internal displacement coordinates.
88 citations
TL;DR: The problem of finding a real, diagonal matrix M such that A + M has prescribed eigenvalues where A is any given symmetric matrix is studied in this paper, where upper and lower bounds are given for the eigen values of a symmetric matrices, obtained by the iterative application of Temple's theorem.
44 citations
TL;DR: In this paper, the authors considered the case of a perturbation Y of arbitrary finite rank and gave sufficient conditions under which an embedded eigenvalue h, of a self-adjoint operator T, of simple multiplicity vanishes under perturbations by I' (Theorem I), and the main tool in the proof was the formula (1.0.6) for the inverse of the Weinstein-Aronszajn matrix W(z).
17 citations
CERN1
TL;DR: In this paper, a simple but efficient computational procedure for calculating bound state solutions of wave equations, valid even for absorptive interactions and corresponding complex eigenvalues, is given. But the integration is deliberately made in the direction of instabilities, but this does not spoil the accuracy.
14 citations
TL;DR: In this article, a method for extracting eigenvalues and eigenvectors of a system using a combination of matrix iteration and matrix decomposition is presented, which is based on the classical procedure for extracting Eigenvalues in ascending or descending order of their magnitude.
Abstract: A method is presented for extracting eigenvalues and eigenvectors of a system using a combination of matrix iteration and matrix decomposition. In addition to the classical procedure for extracting eigenvalues in ascending or descending order of their magnitude, it is shown that eigenvalues can be extracted in a specified region of interest. A new technique for the simultaneous extracting of two or three close eigenvalues which may frequently occur in the neighborhood of a new origin of eigenvalues to which the computations shifted is presented.
9 citations
TL;DR: The eigenvalues of the system matrix are used to construct a matrix which is a transformation in state space between two most frequently used canonical forms as mentioned in this paper, i.e., a transformation between two canonical forms.
Abstract: The eigenvalues of the system matrix are used to construct a matrix which is a transformation in state space between two most frequently used canonical forms.
5 citations
1 citations