Norm of an Operator: Show llTll = max ldl

[mathplease]

Homework Statement

Let D be a nxn diagonal matrix and T:Rⁿ -> Rⁿ be the linear operator associated with D. ie., Tx = Dx for all x in Rⁿ. Show that:

llTll = max ldl

where d1, ..., dn are the entries on the diagonal of D

Homework Equations

the smallest M for which llTxll <= M*llxll is the norm of T

The Attempt at a Solution

i have shown that llTll <= max ldl which was relatively straight forward

im struggling to guess a y such that: llTyll >= maxldl * llyll

which would allow me to conclude that llTll >= max ldl and hence llTll = max ldl

any hints in the right direction is appreciated

 

[mathplease]

actually i think y = e_k where d_k = max |d| works