Normed Vector Space

A normed vector space is a mathematical framework that combines vectors (which can represent points, forces, or other quantities) with a way to measure their size or distance, called a norm. The norm provides a means to quantify how "long" a vector is, similar to measuring the length of a line. This structure allows for various mathematical operations, like adding vectors or scaling them, and helps in understanding concepts like convergence and continuity. Normed vector spaces are foundational in areas like physics, engineering, and computer science, where linear relationships and measurements are essential.