Minkowski inner product matrix ()

Since that is a symmetric bilinear form, the associated matrix is a symmetric matrix.
By default, we will use the time negative representation unless stated otherwise: $$ημν​=⎣⎢⎢⎢⎡​−1000​0100​0010​0001​⎦⎥⎥⎥⎤​ (1)$$ but another equivalent one is to use a time positive representation: $$ημν​=⎣⎢⎢⎢⎡​1000​0−100​00−10​000−1​⎦⎥⎥⎥⎤​ (2)$$ The matrix is typically denoted by the Greek letter eta.