1) It represents the change of basis from one coordinate frame to another.
2) The change of basis can also lead to change in the dimensions of the vector space.
3) The linear map f in the example will not be invertible as the dimensions of the two spaces are different. Is this true for all linear maps which change the dimensions?
Couple of points on the second visualization:-
1) It represents the change of basis from one coordinate frame to another. 2) The change of basis can also lead to change in the dimensions of the vector space. 3) The linear map f in the example will not be invertible as the dimensions of the two spaces are different. Is this true for all linear maps which change the dimensions?