If ||u|| = 3, what's the inner product $u \cdot u$ $u*u$ ?

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Answer 1 · 2017-09-21T17:53:20

For an arbitrary vector $u$ $u$ in a Hilbert space, the norm is defined as,

$| | u | | = \sqrt{u \cdot u}$ $||u|| = sqrt(u*u)$

Thus if $| | u | | = 3$ $||u|| = 3$
$\Rightarrow u \cdot u = 9$ $implies u*u = 9$

If ||u|| = 3, what's the inner product u⋅uu*u?