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Dimensionality: Vectors

The dot product

\[\begin{equation*}
  a = \vec{u} \cdot \vec{v}
\end{equation*}
\]

of two vectors

• \(\vec{u} \in \mathbb{R}^{n}\)
• \(\vec{v} \in \mathbb{R}^{n}\)

is a scalar \(a \in \mathbb{R}\).