normed vector spaces

A normed vector space is a mathematical structure that combines vectors (which can be thought of as arrows in space) with a way to measure their length, called a norm. This allows us to understand concepts like distance and size within that space. For example, in a 2D space, vectors can represent points or directions, and the norm helps us calculate distances between these points. Normed vector spaces are fundamental in various fields, such as physics and computer science, as they provide a framework for solving problems involving directions, distances, and geometric shapes.