In this [page](https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action) there are calculations of variation of Einstein-Hilbert action.


I see variations of terms like this: 



> 
> $\delta {R^{\rho }}\_{{\sigma \mu \nu }}$
> 
> 
> 


where the term is not a functional, and 



> 
> $\frac {\delta {\mathcal {L}}\_{{\mathrm {M}}}}{\delta g^{{\mu \nu }}}$
> 
> 
> 


where we have a functional derivative of a term that is not also a functional.


What is the exact meaning of those expressions?



Variation in Einstein-Hilbert action
It is a notational short hand. (See, e.g. Appendix E in Wald's *General Relativity*). 


Given a function $\psi$ and a one-parameter family of functions $\psi\_{\lambda}$ with $\psi\_0 = \psi$, the notation $\delta \psi$ refers to the short hand $\delta\psi := \frac{d}{d\lambda} \psi\_\lambda \Big|\_{\lambda = 0}$. 


