Inner product space
In mathematics, an inner product space or a Hausdorff pre-Hilbert space is a vector space with a binary operation called an inner product. This operation associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors, often denoted using angle brackets (as in ). Inner products allow the rigorous introduction of intuitive geometrical notions, such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis. Inner product spaces over
Abel's inequalityAbsolute valueAbstract Wiener spaceAcceleration (special relativity)Affine spaceAffine symmetric groupAlgebra over a fieldAlgebraic structureAngleAngles between flatsAnisotropic diffusionAnnihilator (ring theory)Anosov diffeomorphismAuerbach's lemmaBRST quantizationBabuška–Lax–Milgram theoremBalance puzzleBanach spaceBasel problemBasis (linear algebra)Basis functionBent's ruleBessel's inequalityBilinear formBilinear mapBinary functionBochner's theoremBogoliubov inner productBorel functional calculusBracketBracket (mathematics)Bra–ket notationBundle metricC-symmetryCAT(k) spaceCIE 1931 color spaceCanonical correlationCartan–Dieudonné theoremCartesian tensorCauchy product
Link from a Wikipage to another Wikipage
seeAlso
differentFrom
primaryTopic
Inner product space
In mathematics, an inner product space or a Hausdorff pre-Hilbert space is a vector space with a binary operation called an inner product. This operation associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors, often denoted using angle brackets (as in ). Inner products allow the rigorous introduction of intuitive geometrical notions, such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis. Inner product spaces over
has abstract
En matemáticas, un espacio pre ...... ede ser un espacio de Hilbert.
@es
En mathématiques, un espace pr ...... obtenir un espace de Hilbert.
@fr
In de functionaalanalyse, een ...... eerd in de functionaalanalyse.
@nl
In matematica, lo spazio prehi ...... prodotto interno sia completa.
@it
In mathematics, an inner produ ...... f the original inner product .
@en
Inom linjär algebra, är inre p ...... nklar och normen för vektorer.
@sv
Przestrzeń unitarna (prehilber ...... e są czasem prehilbertowskimi.
@pl
Un espai prehilbertià o espai ...... e pot ser un espai de Hilbert.
@ca
Vektorový prostor V nazýváme u ...... ány jako euklidovské prostory.
@cs
Εσωτερικό γινόμενο ονομάζεται ...... γινόμενο του με τον εαυτό του.
@el
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,023,750,263
Link from a Wikipage to another Wikipage
wikiPageUsesTemplate
subject
hypernym
comment
En matemáticas, un espacio pre ...... dirá que es espacio euclídeo.
@es
En mathématiques, un espace pr ...... obtenir un espace de Hilbert.
@fr
In de functionaalanalyse, een ...... eerd in de functionaalanalyse.
@nl
In matematica, lo spazio prehi ...... prodotto interno sia completa.
@it
In mathematics, an inner produ ...... is. Inner product spaces over
@en
Inom linjär algebra, är inre p ...... nklar och normen för vektorer.
@sv
Przestrzeń unitarna (prehilber ...... ich uogólnienie), takich jak:
@pl
Un espai prehilbertià o espai ...... leshores és un espai euclidià.
@ca
Vektorový prostor V nazýváme u ...... ány jako euklidovské prostory.
@cs
Εσωτερικό γινόμενο ονομάζεται ...... γινόμενο του με τον εαυτό του.
@el
label
Espace préhilbertien
@fr
Espacio prehilbertiano
@es
Espai prehilbertià
@ca
Inner product space
@en
Inre produktrum
@sv
Inwendig-productruimte
@nl
Przestrzeń unitarna
@pl
Prähilbertraum
@de
Spazio prehilbertiano
@it
Unitární prostor
@cs