#
nLab
Cauchy–Schwarz inequality

Contents
### Context

#### Linear algebra

**homotopy theory, (∞,1)-category theory, homotopy type theory**

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…

models: topological, simplicial, localic, …

see also **algebraic topology**

**Introductions**

**Definitions**

**Paths and cylinders**

**Homotopy groups**

**Basic facts**

**Theorems**

#### Functional analysis

## Overview diagrams

## Basic concepts

## Theorems

## Topics in Functional Analysis

# Contents

## Statement

Given a real or complex inner product space, we have

$|\langle u,v\rangle|\le \|u\|\cdot\|v\|.$

## Attribution

Known as “Cauchy inequality”, “Cauchy–Schwarz inequality”, “Cauchy–Bouniakowsky–Schwarz” inequality.

Proofs were published by Cauchy in 1821, Bouniakowsky in 1859, Hermann Schwarz in 1888.

## References

Last revised on May 30, 2022 at 14:01:20.
See the history of this page for a list of all contributions to it.