Dot Product

The dot product (also known as the inner product) is an operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

Given two vectors A and B in an n-dimensional space, represented as:

$$\mathbf{A}=\left(\begin{array}{c}{A}_1\\ A_2\\ ⋮\\ A_n\end{array}\right),\mathbf{B}=\left(\begin{array}{c}{B}_1\\ B_2\\ ⋮\\ B_n\end{array}\right)$$

the dot product is defined as:

$$\mathbf{A}\cdot \mathbf{B}=\sum _{i=1}^n{A}_i{B}_i=A_1{B}_1+A_2{B}_2+\cdots +A_n{B}_n$$