hi,
I found one of the notation to be right but I felt a bit addition to explanation of the notation which I am suggesting here.
Given notation was
T : R² =>R³; T(v) = w
Description was
transformation T of a vector v € R² into the vector w € R³ = Perfectly correct
add this statement “where w is vector representation of 3 x2 matrix of vector v in 3D-plane” (FOR BETTER UNDERSTANDING FOR LEARNERS)
Regards
DP
Sorry, but I think that wording is confusing. How can a vector (w in this instance) be a “representation of a 3 x 2 matrix”?
One way to implement such a transformation T would be to define a 3 x 2 matrix A and then you could express that transformation as:
w = A \cdot v
Or
T(v) = A \cdot v
Also note that just because a function maps from \mathbb{R}^2 to \mathbb{R}^3 doesn’t require that it be a linear transformation.
The higher level point is they are just defining some notation here. It’s not required that they explain what transformations are and how they work on the notation sheet. That’s the subject of a whole lecture.
yes I meant the same way, instead of mention T(v) = w, rather mention T(v) =Av
