Euclidean Norm
The Euclidean Norm is a mathematical concept used to measure 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, in a two-dimensional space, the Euclidean Norm of a vector (x, y) is given by \sqrtx^2 + y^2. This norm is commonly used in various fields, including physics and computer science, to quantify distances.
In addition to its applications, the Euclidean Norm is a specific case of the more general concept of p-norms, where p=2. It is named after the ancient Greek mathematician Euclid, who contributed significantly to geometry. The Euclidean Norm is particularly useful in optimization problems and machine learning, where it helps in assessing the similarity or difference between data points.