The term metric signature refers to the signature of a metric tensor g = g_(i j) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative infinitesimal distances of tangent vectors in the tangent bundle of M and which is most easily defined in terms of the signatures of a number of related structures. Most commonly, one identifies the signature of a metric tensor g with the signature of the quadratic form Q_p = 〈·, ·〉_p induced by g on any of the tangent spaces T_p M for points p element M.
Clifford algebra | diagonal matrix | Lorentzian manifold | Lorentzian space | matrix signature | metric tensor | Minkowski space | orthogonal basis | pseudo-Euclidean space | p-signature | quadratic | quadratic form | quadratic form rank | quadratic form signature | smooth manifold | Sylvester's inertia law | Sylvester's signature | tangent bundle | tangent space | tangent vector | vector basis
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