Editing Metric signature (section)

=== Scalar products ===
The standard [[scalar product]] defined on <math> \mathbb{R}^n </math> has the ''n''-dimensional signatures {{nowrap|(''v'', ''p'', ''r'')}}, where {{nowrap|1=''v'' + ''p'' = ''n''}} and rank {{nowrap|1=''r'' = ''0''}}.

In physics, the [[Minkowski space]] is a spacetime manifold <math>\R^4</math> with ''v'' = 1 and ''p'' = 3 bases, and has a scalar product defined by either the <math>\check g</math> matrix:
:<math>\check g=\begin{pmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math>
which has signature <math>(1, 3, 0)^-</math> and known as space-supremacy or space-like; or the mirroring signature <math>(1,3, 0)^+</math>, known as virtual-supremacy or time-like with the <math>\hat g</math> matrix. 
:<math>\hat g=\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}=-\check g</math>