
coordinate
im very lost with transition matrix..thought i understand it alr but turns out i haven..
if i define T to be the transition matrix from S to S'
then let (v)_s be the coordinate vector wrt to S...
then its right of me to say that the coord vector wrt to S' is T(v)_s right?
let S= {v_1,...,v_n}, S' = {v'_1,...,v'_n} be the basis for the vector space V
then in my notes, it states that (v_1,...,v_n) = (v'_1,...,v'_n)T. but i thought it should be
T(v_1,...,v_n) = (v'_1,...,v'_n) since T is from S to S'?
i dont get what it means when my prof puts the T behind the vectors.

Perhaps this example for a vector space with may help you:
Let be two basis of .
Suppose:
Denote:
: coordinates of in respect to
coordinates of in respect to
Then:
Identifying coordinates on , we easily obtain:
Or equivalently:
It's easy to generalize for .
Regards.