Whilst going through the solutions to a GR worksheet, I struggled to understand a lie in the solutions. The line is:
$g_{\sigma[{\mu}}\nabla_{|\rho|}R_{\nu]}^\rho=\frac{1}{2}(g_{\sigma\mu}\nabla_\rho R_\nu^\rho - g_{\sigma\nu}\nabla_\rho R_\mu^\rho)$
where $g$ is the metric, $\nabla$ is the covariant derivative and $R$ is the Ricci tensor. I am working in an n-dimensional manifold equipped with the Levi-Civita connection. The [...] brackets mean to antisymmetrise the indices inside, and the |...| means to leave that indice out of the antisymmetrisation (hence by $\nabla_\rho$ has not changed indice.)
I do not understand is where the factor of $1/2$ came from. Is this just convention or is there a deeper meaning to it?