Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Orthonormal_basis> ?p ?o }
- Orthonormal_basis abstract "In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space Rn is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for Rn arises in this fashion.For a general inner product space V, an orthonormal basis can be used to define normalized orthogonal coordinates on V. Under these coordinates, the inner product becomes dot product of vectors. Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of Rn under dot product. Every finite-dimensional inner product space has an orthonormal basis, which may be obtained from an arbitrary basis using the Gram–Schmidt process.In functional analysis, the concept of an orthonormal basis can be generalized to arbitrary (infinite-dimensional) inner product spaces (or pre-Hilbert spaces). Given a pre-Hilbert space H, an orthonormal basis for H is an orthonormal set of vectors with the property that every vector in H can be written as an infinite linear combination of the vectors in the basis. In this case, the orthonormal basis is sometimes called a Hilbert basis for H. Note that an orthonormal basis in this sense is not generally a Hamel basis, since infinite linear combinations are required. Specifically, the linear span of the basis must be dense in H, but it may not be the entire space.If we go on to Hilbert spaces, a non-orthonormal set of vectors having the same linear span as an orthonormal basis may not be a basis at all. For instance, any square-integrable function on the interval [−1, 1] can be expressed as an infinite sum of Legendre polynomials (an orthonomal basis), but not necessarily as an infinite sum of the monomials xn.".
- Orthonormal_basis wikiPageID "195063".
- Orthonormal_basis wikiPageLength "8785".
- Orthonormal_basis wikiPageOutDegree "54".
- Orthonormal_basis wikiPageRevisionID "683588818".
- Orthonormal_basis wikiPageWikiLink 2-norm.
- Orthonormal_basis wikiPageWikiLink Basis_(linear_algebra).
- Orthonormal_basis wikiPageWikiLink Bijection.
- Orthonormal_basis wikiPageWikiLink Bijective.
- Orthonormal_basis wikiPageWikiLink Cardinal_number.
- Orthonormal_basis wikiPageWikiLink Category:Fourier_analysis.
- Orthonormal_basis wikiPageWikiLink Category:Functional_analysis.
- Orthonormal_basis wikiPageWikiLink Category:Linear_algebra.
- Orthonormal_basis wikiPageWikiLink Countable.
- Orthonormal_basis wikiPageWikiLink Countable_set.
- Orthonormal_basis wikiPageWikiLink Dense_set.
- Orthonormal_basis wikiPageWikiLink Dimension_(linear_algebra).
- Orthonormal_basis wikiPageWikiLink Dimension_(vector_space).
- Orthonormal_basis wikiPageWikiLink Dimension_theorem_for_vector_spaces.
- Orthonormal_basis wikiPageWikiLink Dot_product.
- Orthonormal_basis wikiPageWikiLink Euclidean_space.
- Orthonormal_basis wikiPageWikiLink Exponential_function.
- Orthonormal_basis wikiPageWikiLink Fourier_series.
- Orthonormal_basis wikiPageWikiLink Functional_analysis.
- Orthonormal_basis wikiPageWikiLink Generalized_Fourier_series.
- Orthonormal_basis wikiPageWikiLink Gram–Schmidt_process.
- Orthonormal_basis wikiPageWikiLink Hamel_basis.
- Orthonormal_basis wikiPageWikiLink Hilbert_space.
- Orthonormal_basis wikiPageWikiLink Image_(mathematics).
- Orthonormal_basis wikiPageWikiLink Infinite_linear_combination.
- Orthonormal_basis wikiPageWikiLink Inner_product_space.
- Orthonormal_basis wikiPageWikiLink K-frame.
- Orthonormal_basis wikiPageWikiLink Legendre_polynomials.
- Orthonormal_basis wikiPageWikiLink Linear_algebra.
- Orthonormal_basis wikiPageWikiLink Linear_combination.
- Orthonormal_basis wikiPageWikiLink Linear_map.
- Orthonormal_basis wikiPageWikiLink Linear_operator.
- Orthonormal_basis wikiPageWikiLink Linear_span.
- Orthonormal_basis wikiPageWikiLink Mathematics.
- Orthonormal_basis wikiPageWikiLink Monomial.
- Orthonormal_basis wikiPageWikiLink Norm_(mathematics).
- Orthonormal_basis wikiPageWikiLink Orthogonal_coordinates.
- Orthonormal_basis wikiPageWikiLink Orthogonal_group.
- Orthonormal_basis wikiPageWikiLink Orthogonal_matrix.
- Orthonormal_basis wikiPageWikiLink Orthogonal_transformation.
- Orthonormal_basis wikiPageWikiLink Orthonormal.
- Orthonormal_basis wikiPageWikiLink Orthonormality.
- Orthonormal_basis wikiPageWikiLink Parsevals_identity.
- Orthonormal_basis wikiPageWikiLink Pre-Hilbert_space.
- Orthonormal_basis wikiPageWikiLink Principal_homogeneous_space.
- Orthonormal_basis wikiPageWikiLink Reflection_(mathematics).
- Orthonormal_basis wikiPageWikiLink Rotation_(mathematics).
- Orthonormal_basis wikiPageWikiLink Schauder_basis.
- Orthonormal_basis wikiPageWikiLink Separable_metric_space.
- Orthonormal_basis wikiPageWikiLink Separable_space.
- Orthonormal_basis wikiPageWikiLink Square-integrable_function.
- Orthonormal_basis wikiPageWikiLink Standard_basis.
- Orthonormal_basis wikiPageWikiLink Stiefel_manifold.
- Orthonormal_basis wikiPageWikiLink Sturm–Liouville_eigenproblem.
- Orthonormal_basis wikiPageWikiLink Sturm–Liouville_theory.
- Orthonormal_basis wikiPageWikiLink Total_set.
- Orthonormal_basis wikiPageWikiLink Uncountable_set.
- Orthonormal_basis wikiPageWikiLink Unit_vector.
- Orthonormal_basis wikiPageWikiLink Zorns_lemma.
- Orthonormal_basis wikiPageWikiLinkText "''complete''".
- Orthonormal_basis wikiPageWikiLinkText "Orthonormal basis".
- Orthonormal_basis wikiPageWikiLinkText "Orthonormal_basis#Incomplete_orthogonal_sets".
- Orthonormal_basis wikiPageWikiLinkText "basis".
- Orthonormal_basis wikiPageWikiLinkText "complete basis".
- Orthonormal_basis wikiPageWikiLinkText "complete orthonormal system".
- Orthonormal_basis wikiPageWikiLinkText "complete set of basis states".
- Orthonormal_basis wikiPageWikiLinkText "complete".
- Orthonormal_basis wikiPageWikiLinkText "completeness".
- Orthonormal_basis wikiPageWikiLinkText "orthogonal basis".
- Orthonormal_basis wikiPageWikiLinkText "orthogonal unit vectors".
- Orthonormal_basis wikiPageWikiLinkText "orthonormal bases".
- Orthonormal_basis wikiPageWikiLinkText "orthonormal basis".
- Orthonormal_basis wikiPageWikiLinkText "orthonormal coordinate system".
- Orthonormal_basis wikiPageWikiLinkText "orthonormal transformation matrix".
- Orthonormal_basis wikiPageWikiLinkText "orthonormal".
- Orthonormal_basis wikiPageWikiLinkText "orthonormalising".
- Orthonormal_basis wikiPageWikiLinkText "representations".
- Orthonormal_basis hasPhotoCollection Orthonormal_basis.
- Orthonormal_basis wikiPageUsesTemplate Template:Langle.
- Orthonormal_basis wikiPageUsesTemplate Template:Main.
- Orthonormal_basis wikiPageUsesTemplate Template:Rangle.
- Orthonormal_basis wikiPageUsesTemplate Template:Reflist.
- Orthonormal_basis subject Category:Fourier_analysis.
- Orthonormal_basis subject Category:Functional_analysis.
- Orthonormal_basis subject Category:Linear_algebra.
- Orthonormal_basis hypernym Basis.
- Orthonormal_basis type MeanOfTransportation.
- Orthonormal_basis type Function.
- Orthonormal_basis comment "In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space Rn is an orthonormal basis, where the relevant inner product is the dot product of vectors.".
- Orthonormal_basis label "Orthonormal basis".
- Orthonormal_basis sameAs قاعدة_ممنطمة_متعامدة.
- Orthonormal_basis sameAs Base_ortonormal.
- Orthonormal_basis sameAs Ortonormální_báze.
- Orthonormal_basis sameAs Orthonormalbasis.
- Orthonormal_basis sameAs Base_ortonormal.