Chapter 6  Numerical Linear Algebra


Gerschgorin Circle Theorem


   This software is designed to illustrate Gerschgorin Circle Theorem. Quoted from 1:

   Let  be an  matrix and let  denote the circle in the complex plane with center  and radius ; that is,


where  is used to denote the complex plane. The eigenvalues of  are contained within . Moreover, the union of any  of these circles that do not intersect the remaining  must contain precisely  (counting multiplicities) of the eigenvalues.




【1】         R. L. Burden and J. D. Faires, Numerical Analysis, PWS, Boston, 1993.