I have to do a proof ("Let V be a vector space with basis A, B, C. Show that $T_{AC} = T_{BC}T_{AB}.$
Well, I really don't know what is menat by $"T_{AB}"$ or something like this. I thought about the transformation of matrices.. But what exactly does this mean?
(In order to make the proof I should understand what it says :D )
Thank you very much for any sort of help!
Most probably (read it in your notes/book) it means:
$\;T_{AB}:=$ the transition matrix from basis $\;A\;$ to basis $\;B\;$ = write each element of $\;B\;$ as a linear combination of elements of $\;A\;$ and take the coefficients matrix's transpose.
And likewise with the other ones.