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pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space is a finite-dimensional real $n$ -space together with a non-degenerate quadratic form $q$ . Such a quadratic form can, given a suitable choice of basis $(e 1, \dots, e n)$ , be applied to a vector $x = x 1 e 1 + \dots + x n e n$ , giving
${\\displaystyle q(x)=\\left(x_{1}^{2}+\\dots +x_{k}^{2}\ ight)-\\left(x_{k+1}^{2}+\\dots +x_{n}^{2}\ ight)}$ which is called the scalar square of the vector $x$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Pseudo-Euclidean_space)

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