Vector dot product

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The vector dot product - sometimes called the scalar product, or inner product is defined as follows:


Given two vectors in a finite vector space [ilmath]a,b\in V[/ilmath] where [ilmath]v_i[/ilmath] denotes the [ilmath]i^\text{th} [/ilmath] element of [ilmath]v[/ilmath], the dot product is defined as follows:

[math]a\cdot b=\sum^n_{i=1}a_ib_i[/math]

Other forms

Angle between vectors

[math]a\cdot b=\|a\|\|b\|\cos(\theta)[/math] where [ilmath]\theta[/ilmath] is the angle between the vectors [ilmath]a[/ilmath] and [ilmath]b[/ilmath]