Let be a submultiplicative matrix norm , a diagonalizable matrix with the eigenvalues and a perturbation of . Then every eigenvalue in the spectrum has at most the following distance from the spectrum of :
with the condition number and a matrix that has the eigenvectors of as columns, d. H. .
literature
Robert Plato: Numerical Mathematics compact. Basic knowledge for study and practice. 3. Edition. Vieweg, Braunschweig et al. 2006, ISBN 978-3-8348-0277-4 , section 12.2.1, p. 312f.