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

Contents

Statement

Given a real or complex inner product space, we have

|u,v|uv.|\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.