DLA Terminology and notation

Section 12.2 Terminology and notation

norm (of a vector $v$ ): the quantity $‖ v ‖ = \sqrt{v_{1}^{2} + v_{2}^{2} + \dots + v_{n}^{2}};$ also called the length or magnitude of $v$
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unit vector: a vector whose norm is equal to $1$
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normalization (of a vector $v$ ): the unit vector $\frac{1}{‖ v ‖} v$
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distance (between two vectors $u$ and $v$ ): the distance between the terminal points of the two vectors when their initial points are placed at the same point; can be computed as $‖ u - v ‖$ (or equivalently as $‖ v - u ‖$ )
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dot product (of two vectors $u$ and $v$ of the same dimension): the quantity
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$u \cdot v = u_{1} v_{1} + u_{2} v_{2} + \dots + u_{n} v_{n};$

also referred to as the Euclidean inner product or standard inner product of $u$ and $v$
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angle (between two vectors $u$ and $v$ of the same dimension): the angle $θ$ satisfying both
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$\begin{aligned} 0 & \leq θ \leq π & and & \cos θ & = \frac{u \cdot v}{‖ u ‖ ‖ v ‖} \end{aligned}$

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