The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I = max_(W element S)(dim W) where the set S is defined to be S = {W:W is a subspace of V and g|_W is negative definite}.

Lorentzian manifold | metric signature | metric tensor | metric tensor index | quadratic form signature | smooth manifold