- #1
Ad123q
- 19
- 0
Hi
There are two things that are confusing me a bit, and was wondering if anyone could explain them.
Firstly, if we let V1,V2,...,Vn be vectors in some field F^n and let P = {V1,V2,...,Vn},
then the following are equivalent:
(i) {V1,V2,...,Vn} is a basis for F^n ;
(ii) P is invertible.
Secondly, let T be a linear map. Then if T is invertible, then it is injective.
Thanks for the hep in advance!
There are two things that are confusing me a bit, and was wondering if anyone could explain them.
Firstly, if we let V1,V2,...,Vn be vectors in some field F^n and let P = {V1,V2,...,Vn},
then the following are equivalent:
(i) {V1,V2,...,Vn} is a basis for F^n ;
(ii) P is invertible.
Secondly, let T be a linear map. Then if T is invertible, then it is injective.
Thanks for the hep in advance!