A class of matrix norms, denoted , is defined as
The matrix -norms are defined in terms of the vector -norms (http://planetmath.org/VectorPNorm).
An alternate definition is
As with vector -norms, the most important are the 1, 2, and norms. The 1 and norms are very easy to calculate for an arbitrary matrix:
It directly follows from this that .
The calculation of the -norm is more complicated. However, it can be shown that the 2-norm of is the square root of the largest eigenvalue of . There are also various inequalities that allow one to make estimates on the value of :
( is the Frobenius matrix norm)
|Date of creation||2013-03-22 11:43:22|
|Last modified on||2013-03-22 11:43:22|
|Last modified by||mathcam (2727)|