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In mathematics and theoretical physics, a pseudo-Euclidean space of signature (k, n − k) 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 (e1, ..., en), be applied to a vector x = x1e1 + ⋯ + xnen, giving
which is called the scalar square of the vector x.
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