The p-norm is a generalization of the Euclidean norm in a vector space, defined as the p-th root of the sum of the absolute values of the vector's components raised to the power of p. It provides a flexible way to measure vector magnitude, with special cases including the Manhattan norm (p=1), Euclidean norm (p=2), and the maximum norm (p=∞).

P-norm

p-norm

The Euclidean Norm, also known as the L2 norm or Euclidean length, is a measure of the magnitude of a vector in Euclidean space, calculated as the square root of the sum of the squares of its components. It is widely used in various fields such as machine learning, physics, and computer graphics for measuring distances and optimizing algorithms.

Euclidean norm

A vector space is a mathematical structure formed by a collection of vectors, which can be added together and multiplied by scalars, adhering to specific axioms such as associativity, commutativity, and distributivity. It provides the foundational framework for linear algebra, enabling the study of linear transformations, eigenvalues, and eigenvectors, which are crucial in various fields including physics, computer science, and engineering.

vector space

Vector magnitude, often referred to as the length or size of a vector, is a measure of how much of a quantity is described by the vector, independent of its direction. It is calculated as the square root of the sum of the squares of its components, representing the Euclidean distance from the origin to the point defined by the vector in space.

vector magnitude

Manhattan norm

The maximum norm is a way to measure how big something is by looking at the biggest number in a list. It's like finding the tallest tree in a forest to know how tall the forest can be.

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