- #1
ergonomics
- 14
- 0
If i am given a linear transformation D:A->A,that is followed by
A=ImD(+)kerD
and i am asked to prove that kerD^2=kerD and imD=imD^2.
instead of trying to work it out the hard way by showing that every element of KerD is an element of kerD^2 , both directions.
would it not be easier to just say that dimA=dimA and hence the two structures are isomorphic which means that KerD={0} and ImD=A.
same goes for D^2:A->A
KerD^2={0}
ImD^2=A
=> therefore KerD^2=KerD and ImD^2=ImD ?
A=ImD(+)kerD
and i am asked to prove that kerD^2=kerD and imD=imD^2.
instead of trying to work it out the hard way by showing that every element of KerD is an element of kerD^2 , both directions.
would it not be easier to just say that dimA=dimA and hence the two structures are isomorphic which means that KerD={0} and ImD=A.
same goes for D^2:A->A
KerD^2={0}
ImD^2=A
=> therefore KerD^2=KerD and ImD^2=ImD ?