Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Spectral_theorem> ?p ?o }
- 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 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). Intuitively, diagonal matrices are computationally quite manageable, so it is of interest to see whether an arbitrary matrix can be diagonalized. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector 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 modeled 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. In addition, Cauchy was the first to be systematic about determinants. The spectral theorem as generalized by John von Neumann is today perhaps the most important result of operator theory.This article mainly focuses on 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.".
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- Spectral_theorem wikiPageExternalLink spectral.pdf.
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- Spectral_theorem wikiPageWikiLink Augustin-Louis_Cauchy.
- Spectral_theorem wikiPageWikiLink Augustin_Louis_Cauchy.
- Spectral_theorem wikiPageWikiLink Barry_Simon.
- Spectral_theorem wikiPageWikiLink Bounded_operator.
- Spectral_theorem wikiPageWikiLink C*-algebra.
- Spectral_theorem wikiPageWikiLink Canonical_form.
- Spectral_theorem wikiPageWikiLink Category:Linear_algebra.
- Spectral_theorem wikiPageWikiLink Category:Matrix_theory.
- Spectral_theorem wikiPageWikiLink Category:Singular_value_decomposition.
- Spectral_theorem wikiPageWikiLink Category:Spectral_theory.
- Spectral_theorem wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Spectral_theorem wikiPageWikiLink Characteristic_polynomial.
- Spectral_theorem wikiPageWikiLink Compact_operator.
- Spectral_theorem wikiPageWikiLink Complex_number.
- Spectral_theorem wikiPageWikiLink Conjugate_transpose.
- Spectral_theorem wikiPageWikiLink Diagonal_matrix.
- Spectral_theorem wikiPageWikiLink Diagonalizable_matrix.
- Spectral_theorem wikiPageWikiLink Differential_operator.
- Spectral_theorem wikiPageWikiLink Differential_operators.
- Spectral_theorem wikiPageWikiLink Eigendecomposition_of_a_matrix.
- Spectral_theorem wikiPageWikiLink Eigenvalue.
- Spectral_theorem wikiPageWikiLink Eigenvalues.
- Spectral_theorem wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Spectral_theorem wikiPageWikiLink Eigenvector.
- Spectral_theorem wikiPageWikiLink Ess_sup.
- Spectral_theorem wikiPageWikiLink Essential_supremum_and_essential_infimum.
- Spectral_theorem wikiPageWikiLink Fourier_transform.
- Spectral_theorem wikiPageWikiLink Functional_analysis.
- Spectral_theorem wikiPageWikiLink Fundamental_theorem_of_algebra.
- Spectral_theorem wikiPageWikiLink Gerald_Teschl.
- Spectral_theorem wikiPageWikiLink Hermitian_adjoint.
- Spectral_theorem wikiPageWikiLink Hermitian_conjugate.
- Spectral_theorem wikiPageWikiLink Hermitian_matrix.
- Spectral_theorem wikiPageWikiLink Hermitian_operator.
- Spectral_theorem wikiPageWikiLink Hilbert_space.
- Spectral_theorem wikiPageWikiLink Inner_product.
- Spectral_theorem wikiPageWikiLink Inner_product_space.
- Spectral_theorem wikiPageWikiLink Invariant_subspace.
- Spectral_theorem wikiPageWikiLink John_von_Neumann.
- Spectral_theorem wikiPageWikiLink Jordan_normal_form.
- Spectral_theorem wikiPageWikiLink Linear_algebra.
- Spectral_theorem wikiPageWikiLink Linear_map.
- Spectral_theorem wikiPageWikiLink Linear_operator.
- Spectral_theorem wikiPageWikiLink Mathematical_analysis.
- Spectral_theorem wikiPageWikiLink Mathematics.
- Spectral_theorem wikiPageWikiLink Matrix_(mathematics).
- Spectral_theorem wikiPageWikiLink Matrix_decomposition.
- Spectral_theorem wikiPageWikiLink Measure_(mathematics).
- Spectral_theorem wikiPageWikiLink Measure_space.
- Spectral_theorem wikiPageWikiLink Michael_C._Reed.
- Spectral_theorem wikiPageWikiLink Multiplication_operator.
- Spectral_theorem wikiPageWikiLink Multiplier_(Fourier_analysis).
- Spectral_theorem wikiPageWikiLink Normal_matrix.
- Spectral_theorem wikiPageWikiLink Normal_operator.
- Spectral_theorem wikiPageWikiLink Operator_(mathematics).
- Spectral_theorem wikiPageWikiLink Operator_theory.
- Spectral_theorem wikiPageWikiLink Orthogonal_complement.
- Spectral_theorem wikiPageWikiLink Orthogonal_projection.
- Spectral_theorem wikiPageWikiLink Orthonormal_basis.
- Spectral_theorem wikiPageWikiLink Paul_Halmos.
- Spectral_theorem wikiPageWikiLink Projection-valued_measure.
- Spectral_theorem wikiPageWikiLink Projection_(linear_algebra).
- Spectral_theorem wikiPageWikiLink Real_number.
- Spectral_theorem wikiPageWikiLink Schur_decomposition.
- Spectral_theorem wikiPageWikiLink Self-adjoint.
- Spectral_theorem wikiPageWikiLink Self-adjoint_operator.
- Spectral_theorem wikiPageWikiLink Self-adjoint_operators.
- Spectral_theorem wikiPageWikiLink Sheldon_Axler.
- Spectral_theorem wikiPageWikiLink Singular_value_decomposition.
- Spectral_theorem wikiPageWikiLink Spectral_measure.
- Spectral_theorem wikiPageWikiLink Spectral_theory.
- Spectral_theorem wikiPageWikiLink Spectral_theory_of_ordinary_differential_equations.
- Spectral_theorem wikiPageWikiLink Symmetric_matrix.
- Spectral_theorem wikiPageWikiLink Theorem.
- Spectral_theorem wikiPageWikiLink Unitary_matrix.
- Spectral_theorem wikiPageWikiLinkText "Spectral Theorem".
- Spectral_theorem wikiPageWikiLinkText "Spectral theorem".
- Spectral_theorem wikiPageWikiLinkText "eigenvalue decomposition".
- Spectral_theorem wikiPageWikiLinkText "resolvent".
- Spectral_theorem wikiPageWikiLinkText "spectral decomposition".
- Spectral_theorem wikiPageWikiLinkText "spectral measure".
- Spectral_theorem wikiPageWikiLinkText "spectral projection".
- Spectral_theorem wikiPageWikiLinkText "spectral theorem for compact self-adjoint operators".
- Spectral_theorem wikiPageWikiLinkText "spectral theorem".
- Spectral_theorem wikiPageWikiLinkText "spectral theory".
- Spectral_theorem wikiPageWikiLinkText "spectrum".
- Spectral_theorem date "May 2015".
- Spectral_theorem hasPhotoCollection Spectral_theorem.
- Spectral_theorem reason "It is unclear whether this statement is restating the previous theorem, or is describing a new theorem. If the latter, then in order to distinguish this new theorem from previous versions, the word "simple" needs to be made more precise.".
- Spectral_theorem reason "These are called symmetric matrices in the real case. The entire section uses terminology of the complex case, improperly applying it simultaneously to the real case.".
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