The $\mathrm{L}^1$ norm of a vector $\mathbf{x} = (x_1, x_2, \ldots, x_n)$ in $\mathbb{R}^n$ is defined as $\|\mathbf{x}\|_1 = |x_1| + |x_2| + \cdots + |x_n|$. This norm measures the sum of the absolute values of the components of the vector.
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