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Derive the expression for following questions. Do not write the answers directly. (a) Let A Rnn, x Rn. Compute (xT Ax)x. (b) Let x Rn.
Derive the expression for following questions. Do not write the answers directly.
(a) Let A Rnn, x Rn. Compute (xT Ax)x.
(b) Let x Rn. Prove that ||x||2 ||x||1 n||x||2. (Hint: The Cauchy-Schwarz inequality may come in handy.)
(c)Write down a simple expression for g(x) = sup||z||1(a even smaller 1)1 xTz. Hint: first prove an upper bound on g(x), then propose a choice of z that achieves the bound.
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