= Minkowski inner product matrix
{c}
{title2=$\eta_{\mu\nu}$}
The <matrix representation of the symmetric bilinear form> that is the <Minkowski inner product>.
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:
$$
\eta_{\mu\nu} =
\begin{bmatrix}
-1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}
$$
but another equivalent one is to use a time positive representation:
$$
\eta_{\mu\nu} =
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 \\
\end{bmatrix}
$$
The matrix is typically denoted by the <eta>[Greek letter eta].