A well known result from linear algebra (http://planetmath.org/SylvestersLaw) permits us to make a change of basis such that in the new base is represented by a diagonal matrix with or elements in the diagonal. If there are , elements in the diagonal and , , the tensor is said to have signature
Pseudo-Riemannian manifolds are crucial in Physics and in particular in General Relativity where space-time is modeled as a 4-pseudo Riemannian manifold with signature (1,3)11also referred to as .
Intuitively pseudo-Riemannian manifolds are generalizations of Minkowski’s space just as a Riemannian manifold is a generalization of a vector space with a positive definite metric.
|Date of creation||2013-03-22 15:44:15|
|Last modified on||2013-03-22 15:44:15|
|Last modified by||cvalente (11260)|