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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 wikiPageRevisionID "605237152".
- Metric_signature hasPhotoCollection Metric_signature.
- Metric_signature subject Category:Differential_geometry.
- Metric_signature subject Category:Metric_tensors.
- Metric_signature type Abstraction100002137.
- Metric_signature type Cognition100023271.
- Metric_signature type Concept105835747.
- Metric_signature type Content105809192.
- Metric_signature type Idea105833840.
- Metric_signature type MetricTensors.
- Metric_signature type PsychologicalFeature100023100.
- Metric_signature type Quantity105855125.
- Metric_signature type Tensor105864481.
- Metric_signature type Variable105857459.
- 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 "Assinatura métrica".
- Metric_signature label "Metric signature".
- Metric_signature label "Segnatura (algebra lineare)".
- Metric_signature label "Signatur (Lineare Algebra)".
- Metric_signature label "Signatuur (natuurkunde)".
- Metric_signature label "Сигнатура (линейная алгебра)".
- Metric_signature sameAs Signatur_(Lineare_Algebra).
- Metric_signature sameAs Segnatura_(algebra_lineare).
- Metric_signature sameAs 계량_부호수.
- Metric_signature sameAs Signatuur_(natuurkunde).
- Metric_signature sameAs Assinatura_métrica.
- Metric_signature sameAs m.02ck1_.
- Metric_signature sameAs Q1142562.
- Metric_signature sameAs Q1142562.
- Metric_signature sameAs Metric_signature.
- Metric_signature wasDerivedFrom Metric_signature?oldid=605237152.
- Metric_signature isPrimaryTopicOf Metric_signature.