I am not entirely sure about the change, but I think the matrix J is mapping from C to B:
i.e.
x = x1 c1 + x2 c2 = y1 b1 + y2 b2 = y
so vector x is a coordinate vector w.r.t. (c1, c2) and y is a coordinate vector w.r.t. (b1, b2).
I am a newbie and this is quite confusing to me, please explain if I am wrong, thanks a lot.
I am not entirely sure about the change, but I think the matrix J is mapping from C to B: i.e. x = x1 c1 + x2 c2 = y1 b1 + y2 b2 = y so vector x is a coordinate vector w.r.t. (c1, c2) and y is a coordinate vector w.r.t. (b1, b2).
I am a newbie and this is quite confusing to me, please explain if I am wrong, thanks a lot.