Refined Interlacing Properties
CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS
Pagination or Media Count:
As for back as 1821, in the Cours dAnalyze of the Ecole Polytechnique, Augustin Cauchy published a proof of the following remarkable result. If any row, together with its matching column, is deleted from a real symmetric matrix, then the eigenvalues of the new matrix interlace the eigenvalues of the old one. In the presence of more information, much more can be said about the interlacing of eigenvalues and the relationship between the space and the corresponding eigenvectors. An example of such results can be found in a 1972 paper by G. H. Golub which discusses aspects of the Lanczos algorithm.
- Numerical Mathematics