Dot Product

linear-algebra

Definition

Dot Product

The dot product of two vectors $\mathbf{a},\mathbf{b}\in V$, where $V$ is a vector space, is the sum of the products of the corresponding elements:

$$\mathbf{a}\cdot \mathbf{b}=\sum _{i=1}^n{\mathbf{a}}_i\cdot {\mathbf{b}}_i$$

The result is a scalar in the scalar field of the vector space $V$.

Similarity

The dot product can be viewed as a measurement of similarity of two vectors because it quantifies how much two vectors are aligned. A higher dot product indicates greater degree of alignment or similarity between the vectors.