# Definition The Minkowski metric is a [[Non-Degeneracy (Quadratic Forms)|non-degenerate]] [[Hermitian form]] on $\mathbb{R}^n.$ It is specifically a symmetric, [[Non-Degeneracy (Quadratic Forms)|non-degenerate]] (2,0) [[metric tensor|metric tensor]]. In an *orthonormal [[basis]]*, its matrix takes the form: $ \begin{align} [\eta] = \begin{pmatrix} 1 & & & &0 \\ & 1 & & & \\ & & \ddots & &\\ & & & 1 & \\ 0& & & & -1 \end{pmatrix} \end{align} $ # Sign Convention The matrix form of the Minkowski metric given above is the one often used by mathematicians, where "time" is the last component of the vector. In physics, the sign convention depends on the subfield $ \begin{align} [\eta] = \pm \begin{pmatrix} -1 & & & \\ & 1 & & \\ & & &\\ & & 1 & \\ & & & 1 \end{pmatrix} \end{align} $ See §2.6 Example 2.20 in Jeevanjee for an introduction.