the norm for a linear transformation T on R^n is ||T|| = {max|T(x)| : |x|<= 1} i need to show this is equivalent to ||T|| = {max|T(x)| : |x| = 1}
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Originally Posted by CarmineCortez the norm for a linear transformation T on R^n is ||T|| = {max|T(x)| : |x|<= 1} i need to show this is equivalent to ||T|| = {max|T(x)| : |x| = 1} Let and then where the last inequality follows since and . The other inequality is immediate since . PS. Notice that this proof only requires a normed vector space.
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