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- Spectral_theorem abstract "In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This concept of diagonalization is relatively straightforward for operators on finite-dimensional spaces, but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical perspective.Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces.The spectral theorem also provides a canonical decomposition, called the spectral decomposition, eigenvalue decomposition, or eigendecomposition, of the underlying vector space on which the operator acts.Augustin Louis Cauchy proved the spectral theorem for self-adjoint matrices, i.e., that every real, symmetric matrix is diagonalizable. The spectral theorem as generalized by John von Neumann is today the most important result of operator theory. In addition, Cauchy was the first to be systematic about determinants.In this article we consider mainly the simplest kind of spectral theorem, that for a self-adjoint operator on a Hilbert space. However, as noted above, the spectral theorem also holds for normal operators on a Hilbert space.".
- Spectral_theorem wikiPageExternalLink 2313117.
- Spectral_theorem wikiPageExternalLink ,.
- Spectral_theorem wikiPageExternalLink spectral.pdf.
- Spectral_theorem wikiPageID "123495".
- Spectral_theorem wikiPageRevisionID "595450285".
- Spectral_theorem hasPhotoCollection Spectral_theorem.
- Spectral_theorem subject Category:Linear_algebra.
- Spectral_theorem subject Category:Matrix_theory.
- Spectral_theorem subject Category:Singular_value_decomposition.
- Spectral_theorem subject Category:Spectral_theory.
- Spectral_theorem subject Category:Theorems_in_functional_analysis.
- Spectral_theorem type Abstraction100002137.
- Spectral_theorem type Communication100033020.
- Spectral_theorem type Message106598915.
- Spectral_theorem type Proposition106750804.
- Spectral_theorem type Statement106722453.
- Spectral_theorem type Theorem106752293.
- Spectral_theorem type TheoremsInFunctionalAnalysis.
- Spectral_theorem comment "In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).".
- Spectral_theorem label "Spectraalstelling".
- Spectral_theorem label "Spectral theorem".
- Spectral_theorem label "Spektralsatz".
- Spectral_theorem label "Teorema de descomposición espectral".
- Spectral_theorem label "Teorema spettrale".
- Spectral_theorem label "Teoremas espectrais".
- Spectral_theorem label "Théorème spectral".
- Spectral_theorem label "Twierdzenie spektralne".
- Spectral_theorem label "Спектральная теорема".
- Spectral_theorem label "スペクトル定理".
- Spectral_theorem label "谱定理".
- Spectral_theorem sameAs Spektralsatz.
- Spectral_theorem sameAs Teorema_de_descomposición_espectral.
- Spectral_theorem sameAs Théorème_spectral.
- Spectral_theorem sameAs Teorema_spettrale.
- Spectral_theorem sameAs スペクトル定理.
- Spectral_theorem sameAs Spectraalstelling.
- Spectral_theorem sameAs Twierdzenie_spektralne.
- Spectral_theorem sameAs Teoremas_espectrais.
- Spectral_theorem sameAs m.0x2s0.
- Spectral_theorem sameAs Q1425077.
- Spectral_theorem sameAs Q1425077.
- Spectral_theorem sameAs Spectral_theorem.
- Spectral_theorem wasDerivedFrom Spectral_theorem?oldid=595450285.
- Spectral_theorem isPrimaryTopicOf Spectral_theorem.