Chapter 6  Numerical Linear Algebra


Norm of Vectors and Matrices


   The  and  norms of a vector  are defined by

,  and .


If  is any vector norm on , then  is the definition for a matrix norm. For example, the  norm of a matrix  is defined by . Furthermore, it can be shown that the  and  norms of a  matrix  can be computed by:

,  and , where  is the spectral radius.


   Motivated by Moler’s eigen show, in addition to the eigenvalue and eigenvector, this software shows the geometric meaning of  and  norms of a matrix according to their definitions.




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