About: Orthogonal basis

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In mathematics, particularly linear algebra, an orthogonal basis for an inner product space is a basis for whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis.

Attributes	Values
rdf:type	mean of transportation
rdfs:label	Base ortogonal (ca) Orthogonal basis (en) Base ortogonal (pt) Ортогональный базис (ru) Ортогональний базис (uk)
rdfs:comment	En matemàtiques, en particular en àlgebra lineal, una base ortogonal d'un espai vectorial V amb producte escalar és una base de V els vectors de la qual són ortogonals 2 a 2. Si els vectors d'una base ortogonal són normalitzats, es diu que és base ortonormal. Qualsevol base ortogonal es pot utilitzar per definir un sistema de coordenades ortogonals. Les bases ortogonals (no necessàriament ortonormals) són importants a causa del seu aspecte de curvilínies en espais Euclidians, així com en varietats Riemannianes i pseudo-Riemannianes. (ca) In mathematics, particularly linear algebra, an orthogonal basis for an inner product space is a basis for whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. (en) Em matemática, na teoria da álgebra linear, uma base ortogonal para um espaço vetorial com produto interno V é uma base para V cujos vetores são mutuamente ortogonais. Se os vetores de uma base ortogonal forem normalizados, a base resultante é uma base ortonormal. (pt) Ортогона́льный (ортонорми́рованный) ба́зис — ортогональная (ортонормированная) система элементов линейного пространства со скалярным произведением, обладающая свойством полноты. (ru) Ортогональний базис — система елементів лінійного простору зі скалярним добутком, що має властивість повноти. (uk)
dcterms:subject	Linear algebra Functional analysis
Wikipage page ID	755400 (xsd:integer)
Wikipage revision ID	1119698283 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar (mathematics) Normalize (linear algebra) Basis (linear algebra) Vector space Mathematics Orthogonal Ergebnisse der Mathematik und ihrer Grenzgebiete Orthogonal coordinates Orthogonality Linear algebra Functional analysis Orthonormal basis Linear algebra Curvilinear coordinates Euclidean space Field (mathematics) Quadratic form Pseudo-Riemannian manifold Riemannian manifold Functional analysis Symmetric bilinear form Inner product space Springer-Verlag
sameAs	Orthogonal basis Orthogonal basis Orthogonal basis Orthogonal basis Orthogonal basis Orthogonal basis Orthogonal basis Orthogonal basis
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:MathWorld dbt:Reflist dbt:Functional_analysis dbt:Lang_Algebra dbt:Linear_algebra dbt:Hilbert_space
Link from a Wikipa... related subject.	dbpedia-de:Orthogonalbasis
pages	572 (xsd:integer)
title	Orthogonal Basis (en)
urlname	OrthogonalBasis (en)
edition	3 (xsd:integer)
has abstract	En matemàtiques, en particular en àlgebra lineal, una base ortogonal d'un espai vectorial V amb producte escalar és una base de V els vectors de la qual són ortogonals 2 a 2. Si els vectors d'una base ortogonal són normalitzats, es diu que és base ortonormal. Qualsevol base ortogonal es pot utilitzar per definir un sistema de coordenades ortogonals. Les bases ortogonals (no necessàriament ortonormals) són importants a causa del seu aspecte de curvilínies en espais Euclidians, així com en varietats Riemannianes i pseudo-Riemannianes. (ca) In mathematics, particularly linear algebra, an orthogonal basis for an inner product space is a basis for whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. (en) Em matemática, na teoria da álgebra linear, uma base ortogonal para um espaço vetorial com produto interno V é uma base para V cujos vetores são mutuamente ortogonais. Se os vetores de uma base ortogonal forem normalizados, a base resultante é uma base ortonormal. (pt) Ортогона́льный (ортонорми́рованный) ба́зис — ортогональная (ортонормированная) система элементов линейного пространства со скалярным произведением, обладающая свойством полноты. (ru) Ортогональний базис — система елементів лінійного простору зі скалярним добутком, що має властивість повноти. (uk)
gold:hypernym	Basis
prov:wasDerivedFrom	wikipedia-en:Orthogonal_basis?oldid=1119698283&ns=0
page length (characters) of wiki page	3348 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Orthogonal_basis
is rdfs:seeAlso of	Inner product space
is Link from a Wikipage to another Wikipage of	Pseudo-Euclidean space Basis (linear algebra) Vector space Covariance and contravariance of vectors Generalized Fourier series Wrapped distribution Clifford algebra Eigenvalues and eigenvectors Einstein notation Multipole expansion Orthobasis Orthogonalization Singular value decomposition Sturm–Liouville theory Frobenius characteristic map Fuglede's conjecture Schauder basis Fast wavelet transform Graph Fourier transform Hankel transform Point reflection Pseudo-Riemannian manifold Hermitian matrix Binocular Rivalry Described by Quantum Formalism Biorthogonal system Block transform Mixing angle Discrete Fourier transform Automatic basis function construction Class function Categorical quantum mechanics

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