- #1
Badger33
- 36
- 0
If T:Mnxn ----> Mnxn then dim(T(Mnxn))+dim(ker(T))=dim(Mnxn)
I chose matrices because I thought they would be hardest and I am looking to understand concepts here. Suppose n=2. The dim(Mnxn)=4. Now I need to be able to find the other two values. I also know dim(T(Mnxn))=RANK, well at least I think this is correct. How do I find the rank and the ker. Then once I have the ker how do I find the dim of the ker?
I know this to be linear so let's use this for sake of example:
T:M2x2 ---> M2x2
[a b] |___\ [a a+b]
[c d] | / [c c+d]
Hopefully you can understand all my notation.
I chose matrices because I thought they would be hardest and I am looking to understand concepts here. Suppose n=2. The dim(Mnxn)=4. Now I need to be able to find the other two values. I also know dim(T(Mnxn))=RANK, well at least I think this is correct. How do I find the rank and the ker. Then once I have the ker how do I find the dim of the ker?
I know this to be linear so let's use this for sake of example:
T:M2x2 ---> M2x2
[a b] |___\ [a a+b]
[c d] | / [c c+d]
Hopefully you can understand all my notation.