If is an matrix, and is an vector, then the linear transformation maps n to m so the linear transformation should have a condition number, condAx . Assume that is a subordinate norm. Show that...

If

is an
matrix, and

is an

vector, then the linear transformation

maps

ⁿ
to

^m

so the linear transformation should have a condition number, condAx
. Assume that

is a subordinate norm.

Show that we can define

Find the condition number of the linear transformation at

^T
using thenorm

Show that cond_Ax




^-1

for all

Verify the result of part
for the matrix and vector of part