Matrix Norm and Spectral Norm

new example

φ

A = 

2	4
2	1



||A|| = 4.84416

v = {-0.542971,-0.839751} A . v = {-4.44495,-1.92569}

This Demonstration shows how to find the spectral norm of any 2×2 matrix

A

using the definition

||A

||

2

=

max

||x||=1

||A.x

||

2

. The graphic shows the vectors

x

with

||x

||

2

=1

and their transformations vector

A.x

(red arrows). The green arrows show the vector

v

that gives the maximum and its transformation by

A

.

Eugenio Bravo Sevilla