- #1
mathplease
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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