Definition
Let A be a symmetric matrix of reals. More generally, the metric signature (p, q, r) of A is a set of three natural numbers defined as the number of positive, negative and zero eigenvalues of the matrix counted with regard to their algebraic multiplicity. When r is nonzero the matrix A is called degenerate.
If φ is a scalar product on a finite-dimensional vector space V, the signature of V is the signature of the matrix that represents φ with respect to a chosen basis. According to Sylvester's law of inertia, the signature does not depend on the choice of basis.
Read more about this topic: Metric Signature
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