The L^1 norm, also known as the Manhattan norm or taxicab norm, measures the distance between two points in a space by summing the absolute differences of their coordinates. For a vector x = (x_1, x_2, \ldots, x_n) , the L^1 norm is calculated as ||x||_1 = |x_1| + |x_2| + \ldots + |x_n| . This norm is particularly useful in various fields, including statistics and machine learning, where it helps in optimizing models. In contrast to the L^2 norm, which squares the differences and takes the square root, the L^1 norm emphasizes larger deviations more linearly. This property makes it robust to outliers, as it does not disproportionately weigh larger errors. The L^1 norm is often used in regularization techniques, such as Lasso regression, to promote spars