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steenis

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- TL;DR Summary
- A semidefinite inner product is also positive-definite

I have the followinq question:

Let ##(,)## be a real-valued inner product on a real vector space ##V##. That is, ##(,)## is a symmetric bilinear map ##(,):V \times V \rightarrow \mathbb{R}## that is non-degenerate

Suppose, for all ##v \in V## we have ##(v,v) \geq 0##

Now I want to prove that if ##(x,x)=0## then ##x=0## for ##x \in V##

Can anybody help me ?

Let ##(,)## be a real-valued inner product on a real vector space ##V##. That is, ##(,)## is a symmetric bilinear map ##(,):V \times V \rightarrow \mathbb{R}## that is non-degenerate

Suppose, for all ##v \in V## we have ##(v,v) \geq 0##

Now I want to prove that if ##(x,x)=0## then ##x=0## for ##x \in V##

Can anybody help me ?