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   of the metric tensor with respect to a basis. Alternatively, it can be defined as the dimensions of a maximal positive, negative and null subspace. By Sylvester's law of inertia these numbers do not depend on the choice of basis. The signature thus classifies the metric up to a choice of basis. The signature is often denoted by a pair of integers implying r = 0 or as an explicit list of signs of eigenvalues such as or for the signature resp. .