Recent content by nonne

So, I'm going over this bit in the beginning of MTW's Gravitation where they give an equation for changing acceleration from time coordinate t to time coordinate T(t): \frac{{d}^{2}x}{{dt}^{2}} = \frac{d}{dt}(\frac{dx}{dT}\frac{dT}{dt}) = \frac{{d}^{2}T}{{dt}^{2}}\frac{dx}{dT} +...

Yeah, no, I understand that bit, but does that also mean that: T(sa, tb) = stT(a, b) where s and t are scalars, for a linear operator T with multiple arguments?

So I'm reading these notes about differential geometry as it relates to general relativity. It defines a tensor as being, among other things, a linear scalar function, and soon after it gives the following equation as an example of this property of linearity: T(aP + bQ, cR + dS) = acT(P, R) +...