Minkowski spaceMinkowskiSpace2006-09-23 20:22:462006-09-23 23:24:49Definition% this is the default PlanetMath preamble. as your knowledge
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\emph{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:
\begin{itemize}
\item $M$ is a 4 dimensional real vector space
\item $g$ is a symmetric 2-covariant tensor (defines a quadratic form )
\item $g$ is non-degenerate (i.e. $\forall {x\in M}, g(x,y) = 0 \implies y=0$)
\item the \PMlinkname{diagonalization}{SylvestersLaw} of $g$ contains one negative and three positive diagonal entries\footnote{this convention is sometimes reversed depending on notation}.
\end{itemize}