I am very confused with succinct notations of the transformations in Linear Algebra. When do we write each of the ways? What is the difference?
In the lecture notes it says: T(x) = Ax = b in R^m, where x is an input vector and A is a matrix/transformation.
Notice that A is on the left from x.
But then in the number of occasions I see that input vector(s) is(are) sometimes on the left, even the notation is still T(x). For example:
and here, where bases V were supposed to be an input on the write (Ax) since we perform operation on it:
If you do calculations for the last one you will get:
Also, in support of the T(x) = Ax I found this in the notes:
Thank you.