Inner product on [tex]\mathbb{R}^n[/tex]: Is it P:ℝn×ℝn→ℝ or is it P:ℝn×ℝn→ℝ+ ?

pisrationalhahaha

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Inner product on [tex]\mathbb{R}^n[/tex]: Is it P:ℝn×ℝn→ℝ or is it P:ℝn×ℝn→ℝ+ ?

I am confused about the definition of the inner product
-is it : \(\displaystyle P:\mathbb{R}^n\times \mathbb{R}^n\rightarrow \mathbb{R}\)
-or: \(\displaystyle P:\mathbb{R}^n\times \mathbb{R}^n\rightarrow \mathbb{R} ^+\)
I know that it's \(\displaystyle \mathbb{R} ^+\) from my teacher
why it's \(\displaystyle \mathbb{R} ^+\) ?
An inner product which is also a dot product is negative sometimes if the angle is between pi/2 and 3pi/2
 
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