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.
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In mathematics, the signature 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.
Wolfram MathWorld: Metric signature
Wolfram MathWorldIn Branch: Algebra, Subject classificationsQuote, In Branch: Algebra, Subject classifications
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