Chapter 6 Numerical Linear Algebra
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.
R. L. Burden and J. D. Faires, Numerical Analysis, PWS,