The L² 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 v = (x₁, x₂, ..., xₙ), the L² norm is given by √(x₁² + x₂² + ... + xₙ²). This norm is widely used in various fields, including mathematics, physics, and machine learning. In the context of functional analysis, the L² norm is essential for defining concepts like distance and convergence in spaces of functions. It helps in quantifying how close two functions are to each other. The L² norm is particularly important in signal processing and statistics, where it is used to minimize errors and optimize solutions.