Re: [Algorithms] How to derive transformation matrices

[<ro...@do...>]

I wrote

>  The only formulas that are an
>aid to understanding, ...  are those that are
>manifestly coordinate invariant. 

Albert Einstein took this principle, or rather its extension to
generalized curvilinear coordinates for space-time, which he called 
"The Principle of General Covariance", as his guiding light in
deriving the gravitational field equations of General Relativity.  The
entire framework of classical physics suggests that they must be
second-order partial differential equations.  Einstein arrives at them
as the simplest possible system of second-order PDEs that can be
expressed in a manifestly coordinate invariant way.

Aid to understanding? 85 years of increasingly precise observational
data (mostly astronomical) confirms them in every way.