Definition:Dot Product

Definition
Given any two vectors $$a$$ and $$b$$ in $$\R^n$$, the Dot Product is defined as:


 * $$a \bullet b = a_1 b_1 + a_2 b_2 + \cdots + a_n b_n = \sum_{i-1}^{n} a_i b_i$$

The symbol used for the dot is variously presented; another version is $$a \cdot b$$.

It is also known as:


 * The Scalar Product;
 * The Standard Inner Product.

Some basic properties of the dot product can be found here.

It can be shown that the dot product is an inner product.