Norm (mathematics)

In mathematics, a norm is a function that assigns a non-negative length or size to elements in a vector space. Think of it like measuring the magnitude of a vector, similar to how you might measure the distance from the origin to a point in space. Norms have specific properties: the norm of a vector is zero only if the vector is zero itself, scaling a vector scales its norm proportionally, and the norm of a sum of vectors is at most the sum of their norms. Norms help quantify and analyze the size or length of objects within mathematical spaces.