Inner Dot Product

linear-algebra

Definition

Dot Product

Let $x,y\in {\mathbb{R}}^d$ be vectors of vector space ${\mathbb{R}}^d$. The inner dot product is defined as the scalar:

$$⟨x,y⟩=\sum _{i=1}^d{x}_i{y}_i=x_1{y}_1+x_2{y}_2+\cdots +x_d{y}_d$$

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.