= Pseudo-Riemannian manifold
{wiki=Pseudo-Riemannian_manifold}
A pseudo-Riemannian manifold is a generalization of a Riemannian manifold that allows for the metric tensor to have signature that is not positive definite. While in a Riemannian manifold the metric tensor \\( g \\) is positive definite, which means that for any nonzero tangent vector \\( v \\), the inner product \\( g(v, v) > 0 \\), a pseudo-Riemannian manifold has a metric tensor that can have both positive and negative eigenvalues.
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