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.

 

 

References:

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