Proving that scalar product is non-degenerate

[keen holly]

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[wild moat]

how do you define non-degeneracy?

[wild moat]

and what are you stuck with?

Assume v is nonzero, use continuity of v to find an interval where v is positive, say

and from there you can pick a suitable w such that <v,w> is nonzero

@keen holly

or if you want to prove directly just use the fact that

$$ \int _0^1 v(t)^2dt = 0 $$

[viscid garnet]

aL

[wild moat]

v^2 is nonnegative and continuous

[molten ravine]

and not identically zero

[keen holly]

makes sense ok

ty

+close

[grave delta]

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[grave delta]

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