1. Show that if is an induced matrix norm, then where is an eigenvalue of 2. This problem demonstrates why ∞ is a -norm by showing that 3. Reorder the elements in are the largest elements in...

1. Show that if

is an induced matrix norm, then

where

is an eigenvalue of

2. This problem demonstrates why

_∞
is a
-norm by showing that

3. Reorder the elements in are the largest elements in magnitude, and let |xk+1| , |xk+2| , ... , |x|n be the remaining elements. Show that

and complete the argument.