ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Binary cartesian set product ▼ Binary relation ▼ Map ▼ Operation ▼ N-operation ▼ Binary operation ▼ Enclosed binary operation ▼ Groupoid ▼ Ringoid ▼ Semiring ▼ Ring ▼ Left ring action ▼ Module ▼ Linear combination ▼ Linear map ▼ Multilinear map ▼ Bilinear map ▼ Sesquilinear map ▼ Hermitian map ▼ Hermitian form ▼ Semi-inner product ▼ Inner product ▼ Complex Lebesgue inner product ▼ Lebesgue sequence inner product ▼ Complex dot product operation
Definition D743
Euclidean real dot product operation

Let $\mathbb{R}^{N \times 1}$ be a D5656: Set of real column matrices.
The dot product operation on $\mathbb{R}^{N \times 1}$ is the D4364: Real function $$\mathbb{R}^{N \times 1} \times \mathbb{R}^{N \times 1} \to \mathbb{R}, \quad (x, y) \mapsto x^T y$$

Let $\mathbb{R}^N$ be a D5630: Set of euclidean real numbers.
The dot product operation on $\mathbb{R}^N$ is the D4364: Real function $$\mathbb{R}^N \times \mathbb{R}^N \to \mathbb{R}, \quad (x, y) \mapsto \sum_{n = 1}^N x_n y_n$$
Children
 ▶ D6037: Euclidean real component sum operation