WOLFRAM NOTEBOOK

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
.

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