[線代] 內積

[jacky7987 (憶)]

Let V be a inner product space and T be a linear transformation in V.Show that
there is a M>0 such that ∥Tv∥≦M∥v∥.

感謝大家QAQ

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→ jacky7987   :我打完才發現我剛剛都假設他是有限維度在做...
→ Vulpix      :這定理應該也是有限維度才對的啊...
→ Vulpix      :V=C([0,2pi]), T(f)=f', 用v=sin(n*.)之類的試試看
→ jacky7987   :那如果是有限維度 那M該朝甚麼方向找呢?
→ jacky7987   :原本想說把它換成<v,T*T(v)>
→ jacky7987   :打錯XD          <T^*(T(v)),v>