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I have a simple question about Scalar / Dot product. (http://en.wikipedia.org/wiki/Dot_product)

Say f is a bilinear form. I have to tell if f defines a dot product. I didn't understand what I should do, what does f has to satisfy so it can be called a "dot product" ?

thanks

Jenni201
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  • I hope this isn't a dumb question, but have you tried looking up “dot product” in the index of your textbook and seeing if it refers you to the book's definition of what properties a bilinear form must have to be considered a dot product? – MJD Jun 15 '14 at 19:49
  • Actually, I don't have a textbook (and yes it's a dumb question), sorry I just really don't know its definition, been looking over the internet and thought I'd get some proper answer here – Jenni201 Jun 15 '14 at 19:54
  • You said “I have to tell if $f$ defines a dot product”. Why do you have to do that? – MJD Jun 15 '14 at 19:57
  • That's the question (homework). (I know f(x,y)=...) – Jenni201 Jun 15 '14 at 19:59
  • I didn't mean your question was dumb; I meant I hoped my question wasn't dumb. – MJD Jun 15 '14 at 22:33

1 Answers1

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Let $V$ be a vector space over $\Bbb R$.

A bilinear form $f:V\times V\to\Bbb R$ is a scalar product if it satisfies

  1. $f(x,y)=f(y,x)$ for all $x,y\in V$ (symmetric)
  2. $f(x,x)> 0$ for all nonzero $x\in V$ (positive definite)
Berci
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