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 \begin{equation} \mathbb{R}^{N \times 1} \times \mathbb{R}^{N \times 1} \to \mathbb{R}, \quad (x, y) \mapsto x^T y \end{equation}