Normed Space

A normed space is a mathematical framework where each element, called a vector, has a size or length, measured by a function called a norm. This norm assigns a non-negative number to each vector, indicating its magnitude, similar to the concept of distance or length in everyday space. The key properties are that the length of a zero vector is zero, and the length scales consistently when vectors are multiplied by numbers. Normed spaces provide a structured way to analyze vectors, functions, or points in many areas such as physics, engineering, and mathematics.