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Section 12.2 Terminology and notation

norm (of vector \(\uvec{v} \))
the quantity \(\unorm{v} = \sqrt{ v_1^2 + v_2^2 + \dotsb + v_n^2} \text{;}\) also called the length or magnitude of \(\uvec{v} \)
unit vector
a vector whose norm is equal to \(1 \)
normalization (of vector \(\uvec{v} \))
the unit vector \(\displaystyle \frac{1}{\unorm{v}} \, \uvec{v} \)
distance (between vectors \(\uvec{u}, \uvec{v} \))
the distance between the terminal points of the two vectors when their initial points are placed at the same point; can be computed as \(\norm{ \uvec{u} - \uvec{v} } \) (or equivalently as \(\norm{ \uvec{v} - \uvec{u} } \))
dot product (of vectors \(\uvec{u}, \uvec{v} \) of the same dimension)
the quantity
\begin{equation*} \udotprod{u}{v} = u_1 v_1 + u_2 v_2 + \dotsb + u_n v_n \text{;} \end{equation*}
also referred to as the Euclidean inner product or standard inner product of \(\uvec{u} \) and \(\uvec{v} \)
angle (between vectors \(\uvec{u}, \uvec{v} \) of the same dimension)
the angle \(\theta \) satisfying both
\begin{equation*} 0 \le \theta \le \pi \qquad \text{and} \qquad \cos\theta = \frac{\udotprod{u}{v}}{\unorm{u} \unorm{v}} \end{equation*}
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