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- Metric_signature abstract "The signature (p, q, r) of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix gab of the metric tensor with respect to a basis. Alternatively, it can be defined as the dimensions of a maximal positive, negative and null subspace. By Sylvester's law of inertia these numbers do not depend on the choice of basis. The signature thus classifies the metric up to a choice of basis. The signature is often denoted by a pair of integers (p, q) implying r = 0 or as an explicit list of signs of eigenvalues such as (+, −, −, −) or (−, +, +, +) for the signature (1, 3) resp. (3, 1).The signature is said to be indefinite or mixed if both p and q are nonzero, and degenerate if r is nonzero. A Riemannian metric is a metric with a (positive) definite signature. A Lorentzian metric is one with signature (p, 1), or (1, q).There is another notion of signature of a nondegenerate metric tensor given by a single number s defined as p − q, where p and q are as above, which is equivalent to the above definition when the dimension n = p + q is given or implicit. For example, s = 1 − 3 = −2 for (+, −, −, −) and s = 3 − 1 = +2 for (−, +, +, +).".
- Metric_signature wikiPageID "463225".
- Metric_signature wikiPageLength "9522".
- Metric_signature wikiPageOutDegree "59".
- Metric_signature wikiPageRevisionID "702373831".
- Metric_signature wikiPageWikiLink Basis_(linear_algebra).
- Metric_signature wikiPageWikiLink Category:Differential_geometry.
- Metric_signature wikiPageWikiLink Category:Metric_tensors.
- Metric_signature wikiPageWikiLink Cosmology.
- Metric_signature wikiPageWikiLink Definite_quadratic_form.
- Metric_signature wikiPageWikiLink Degeneracy_(mathematics).
- Metric_signature wikiPageWikiLink Descartes_rule_of_signs.
- Metric_signature wikiPageWikiLink Diagonal_matrix.
- Metric_signature wikiPageWikiLink Diagonalizable_matrix.
- Metric_signature wikiPageWikiLink Dot_product.
- Metric_signature wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Metric_signature wikiPageWikiLink Identity_matrix.
- Metric_signature wikiPageWikiLink Isometry.
- Metric_signature wikiPageWikiLink Kernel_(linear_algebra).
- Metric_signature wikiPageWikiLink Main_diagonal.
- Metric_signature wikiPageWikiLink Mathematics.
- Metric_signature wikiPageWikiLink Matrix_congruence.
- Metric_signature wikiPageWikiLink Metric_tensor.
- Metric_signature wikiPageWikiLink Minkowski_space.
- Metric_signature wikiPageWikiLink Orthogonal_basis.
- Metric_signature wikiPageWikiLink Particle_physics.
- Metric_signature wikiPageWikiLink Proper_time.
- Metric_signature wikiPageWikiLink Pseudo-Riemannian_manifold.
- Metric_signature wikiPageWikiLink Quadratic_form.
- Metric_signature wikiPageWikiLink Quantum_gravity.
- Metric_signature wikiPageWikiLink Riemannian_manifold.
- Metric_signature wikiPageWikiLink Sign_(mathematics).
- Metric_signature wikiPageWikiLink Sign_convention.
- Metric_signature wikiPageWikiLink Spacetime.
- Metric_signature wikiPageWikiLink Special_relativity.
- Metric_signature wikiPageWikiLink Spectral_theorem.
- Metric_signature wikiPageWikiLink Sylvesters_law_of_inertia.
- Metric_signature wikiPageWikiLink Symmetric_bilinear_form.
- Metric_signature wikiPageWikiLink Symmetric_matrix.
- Metric_signature wikiPageWikiLink Theoretical_physics.
- Metric_signature wikiPageWikiLinkText "Euclidean".
- Metric_signature wikiPageWikiLinkText "Metric signature".
- Metric_signature wikiPageWikiLinkText "Metric_signature#Signature_change".
- Metric_signature wikiPageWikiLinkText "indefinite signature".
- Metric_signature wikiPageWikiLinkText "metric signature".
- Metric_signature wikiPageWikiLinkText "metric".
- Metric_signature wikiPageWikiLinkText "mixed signature".
- Metric_signature wikiPageWikiLinkText "mostly pluses signature".
- Metric_signature wikiPageWikiLinkText "signature of the metric".
- Metric_signature wikiPageWikiLinkText "signature".
- Metric_signature wikiPageUsesTemplate Template:=.
- Metric_signature wikiPageUsesTemplate Template:Confusing.
- Metric_signature wikiPageUsesTemplate Template:Math.
- Metric_signature wikiPageUsesTemplate Template:Reflist.
- Metric_signature subject Category:Differential_geometry.
- Metric_signature subject Category:Metric_tensors.
- Metric_signature hypernym Number.
- Metric_signature type Physic.
- Metric_signature type Tensor.
- Metric_signature comment "The signature (p, q, r) of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix gab of the metric tensor with respect to a basis. Alternatively, it can be defined as the dimensions of a maximal positive, negative and null subspace.".
- Metric_signature label "Metric signature".
- Metric_signature sameAs Q1142562.
- Metric_signature sameAs Signatur_(Lineare_Algebra).
- Metric_signature sameAs Segnatura_(algebra_lineare).
- Metric_signature sameAs 符号数.
- Metric_signature sameAs 계량_부호수.
- Metric_signature sameAs Signatuur_(natuurkunde).
- Metric_signature sameAs Assinatura_métrica.
- Metric_signature sameAs m.02ck1_.
- Metric_signature sameAs Сигнатура_(линейная_алгебра).
- Metric_signature sameAs Q1142562.
- Metric_signature wasDerivedFrom Metric_signature?oldid=702373831.
- Metric_signature isPrimaryTopicOf Metric_signature.