Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1, n - 1) metric signature is used, Lorentzian n-space is denoted R^(1, n - 1); the notation R^(n - 1, 1) is used analogously with the metric signature (n - 1, 1). The Lorentzian inner product induces a norm on Lorentzian space, whereby the squared norm of a vector x = (x_0, x_1, ..., x_(n - 1)) has the form left bracketing bar x right bracketing bar = - x_0^2 + x_1^2 + ... + x_(n - 1)^2.

inner product space | light cone | lightlike | Lorentzian inner product | metric signature | negative lightlike | negative timelike | positive definite quadratic form | positive definite tensor | positive lightlike | positive timelike | p-signature | quadratic | quadratic form rank | spacelike | Sylvester's inertia law | Sylvester's signature | timelike