A vector norm is a mathematical function that assigns a non-negative length or size to a vector in a vector space. It helps quantify how "big" a vector is, providing a way to measure distances and angles between vectors. Common types of vector norms include the Euclidean norm, which calculates the straight-line distance from the origin to the point represented by the vector, and the Manhattan norm, which sums the absolute values of the vector's components. Vector norms are essential in various fields, including machine learning, physics, and computer graphics. They are used to optimize algorithms, analyze data, and represent geometric transformations. Understanding vector norms is crucial for working with multidimensional data and ensuring accurate calculations in mathematical modeling.