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What is a norm of a vector?
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If $\mathbf{v}=\left(v_{1}, v_{2}, \ldots, v_{n}\right)$ is a vector in $R^{n}$, then the norm of $\mathbf{v}$ (also called the length of $\mathbf{v}$ or the magnitude of $\mathbf{v}$ ) is denoted by $\|\mathbf{v}\|$, and is defined by the formula $$\|\mathbf{v}\|=\sqrt{v_{1}^{2}+v_{2}^{2}+\cdots+v_{n}^{2}}$$
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