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, which can be useful in various applications, such as physics and computer science. Common types of vector norms include the Euclidean norm, which measures 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 optimization problems and machine learning, where they help assess the performance of algorithms. They also play a crucial role in defining concepts like distance and similarity between vectors. By using vector norms, one can compare different vectors and understand their relationships in a multidimensional space.