Metric signature

The signature of a metric tensor is the number, counted with multiplicity, of positive, negative, and zero eigenvalues of the matrix that represents the metric in some basis. Because this count does not depend on the choice of basis, the signature can be used to classify the metric, and it is written as a set of integers giving the number of positive, negative, and zero eigenvalues respectively. A metric is called indefinite or mixed when it has both positive and negative eigenvalues, and degenerate when it has any zero eigenvalues, with special cases including Riemannian metrics, which are positive definite, and Lorentzian metrics, which are used to describe spacetime in relativity. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/