Interactive visualization of a matrix equation: an adjustable 2 by 2 matrix multiplying a labeled x-y input grid with a unit circle to produce a warped x-y output grid, with the input unit vector achieving maximum stretch shown geometrically and as an explicit numeric matrix multiplication equation, illustrating the operator norm

1.6
0.6
0.3
0.9
×
input space
=
output space
the multiplication that achieves the operator norm
1.600.60 0.300.90
×
0.00 0.00
=
0.00 0.00
 so ∥Av∥ = ∥A∥ = 0.00
Operator norm ||A||
--
the maximizing unit vector v and its image Av