Description: The L1 Norm, also known as the Manhattan norm or the sum of absolute values norm, is a measure of distance in a vector space defined as the sum of the absolute values of the components of a vector. This norm is used to calculate the distance between two points in an n-dimensional space, where each point is represented as a vector. The L1 Norm is particularly useful in contexts where one wants to emphasize the difference in each dimension independently, making it ideal for applications in data analysis and optimization. Unlike the L2 norm, which is based on the square root of the sum of the squares of the components, the L1 Norm can be more robust to outliers, as it does not penalize large differences as much. This characteristic makes it a valuable tool in machine learning and statistical analysis, where data interpretation and error minimization are crucial. In summary, the L1 Norm is a fundamental measure in mathematics and statistics that allows for effective and clear evaluation of distances and differences in a vector space.
