Minkowski space

Minkowski space is a 4 dimensional real vector space with a non-degenerate pseudo-metric of signature $(-+++)$ .

More precisely, $M$ with a metric $g$ is a Minkowski space iff:

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$M$ is a 4 dimensional real vector space
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$g$ is a symmetric 2-covariant tensor (defines a quadratic form )
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$g$ is non-degenerate (i.e. $\forall{x\in M},g(x,y)=0\implies y=0$ )
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the diagonalization (http://planetmath.org/SylvestersLaw) of $g$ contains one negative and three positive diagonal entries¹¹this convention is sometimes reversed depending on notation.