Level repulsion and the dynamical diagonalization of matrices

A set of first-order coupled equations of motion for eigenvalues and eigenvectors of a generic matrix is derived in terms of the equation of motion for the matrix itself. An efficient method of diagonalization is then constructed by defining an appropriate dynamics for the matrix. A comparison with the standard diagonalization method based on Jacobi transformations is made. (C) 2002 Elsevier Science B.V. All rights reserved.Universidade Federal de São Paulo, Inst Fis, BR-08315970 São Paulo, BrazilUniversidade Federal de São Paulo, Inst Fis, BR-08315970 São Paulo, BrazilWeb of Scienc