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Inner product space

In mathematics, an inner product space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in ⟨ a , b ⟩ {\displaystyle \langle a,b\rangle } . Inner products allow formal definitions of intuitive geometric notions, such as…

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Overview

Definition

Examples

Basic results, terminology, and definitions

Orthonormal sequences

Operators on inner product spaces

Generalizations

Related products

Bibliography

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Inner product space

Nodes157
Edges156
Triples55
Avg. degree1.99
Density0.012739
Components1

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Inner product space

Top relations

related to Operators on inner product spaces · 12
Inner product space → All, Ax, Ay, Consequently, Continuous, For, Isometrical, Isometries, Several, Symmetric, The Mazur, Ulam
related to Orthonormal sequences · 10
Inner product space → Gram, In, Let, Recall, Say, Schmidt, That, Then, This, Using
related to Degenerate inner products · 8
Inner product space → Another, If, Naimark, Segal, The, The Gelfand, This, We
related to Euclidean vector space · 5
Inner product space → As, Euclidean, For, If, More
related to Hilbert space · 5
Inner product space → An, Cauchy, Hilbert, The, This
is a · 4
Inner product space → Hilbert space, normed vector space, real or complex vector space endowed with an operation called an inner product, vector space V over the field F together with an inner product
related to Norm properties · 4
Inner product space → Every, In, So, With
related to Real and complex numbers · 3
Inner product space → Among, The, Unlike
related to Definition · 2
Inner product space → An, In
related to Vector spaces with forms · 1
Inner product space → On

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Important terminology

inner product displaystyle space langle rangle vector real mathbb spaces complex linear basis right norm left form map vectors isbn

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Inner product spaceis areal or complex vector space endowed with an operation called an inner product0.90text
Inner product spaceis anormed vector space0.90text
Inner product spaceis aHilbert space0.90text
Inner product spaceis avector space V over the field F together with an inner product0.90text
ininstance ofoften denoted with angle brackets0.80text
Inner product spacerelated to DefinitionIn0.60section
Inner product spacerelated to DefinitionAn0.60section
Inner product spacerelated to Degenerate inner productsIf0.60section
Inner product spacerelated to Degenerate inner productsWe0.60section
Inner product spacerelated to Degenerate inner productsThe0.60section
Inner product spacerelated to Degenerate inner productsThis0.60section
Inner product spacerelated to Degenerate inner productsThe Gelfand0.60section

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