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:

• $M$ is a 4 dimensional real vector space
• $g$ is a symmetric 2-covariant tensor (defines a quadratic form )
• $g$ is non-degenerate (i.e. $\forall {x\in M}, g(x,y) = 0 \implies y=0$
• the diagonalization of $g$ contains one negative and three positive diagonal entries ¹.

Footnotes

... entries¹

this convention is sometimes reversed depending on notation