The L^2 norm, also known as the Euclidean norm, measures the length or magnitude of a vector in a multi-dimensional space. It is calculated by taking the square root of the sum of the squares of its components. For example, for a vector \mathbfv = (x_1, x_2, \ldots, x_n) , the L^2 norm is given by ||\mathbfv||_2 = \sqrtx_1^2 + x_2^2 + \ldots + x_n^2 . This norm is widely used in various fields, including machine learning, statistics, and physics, as it provides a way to quantify distances and similarities between points or data sets. The L^2 norm is particularly useful because it is sensitive to large differences in component values, making it effective for optimization problems and error measurement.