# Dictionary:Dot product

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The dot product (also called inner product or scalar product) of the vectors ${\displaystyle \mathbf {X} =[x_{1},x_{2},...,x_{n}]}$ and ${\displaystyle \mathbf {Y} =[y_{1},y_{2},y_{3},...,y_{n}]}$ is

${\displaystyle \mathbf {X} \cdot \mathbf {Y} =\sum _{i=1}^{n}x_{i}y_{i}=[x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}+\ldots +x_{n}y_{n}]}$.

The dot-product reverse is

${\displaystyle \sum _{i=1}^{n}x_{i}y_{n-(i-1)}=[x_{1}y_{n}+x_{2}y_{n-1}+x_{3}y_{n-2}+\ldots +x_{n}y_{1}]}$.

Compare cross product.