Thread: another question about eigenvalues and linear operators

hi, i have another question, last one - so i hope you won't mind:

i need to prove that:

S and T are two linear operators that can switch sides (ST = TS) over a vector space V.
lambda is a eigenvalue of S. the group W is defined as Ker ((lambda)I - S).
prove that W is contained in T(W).

thanks in advance to anyone who can help.

Originally Posted by vonflex1

hi, i have another question, last one - so i hope you won't mind:

i need to prove that:

S and T are two linear operators that can switch sides (ST = TS) over a vector space V.
lambda is a eigenvalue of S. the group W is defined as Ker ((lambda)I - S).
prove that W is contained in T(W).

thanks in advance to anyone who can help.

are you sure it's not the other way round, i.e. ? that's a trivial result: if then and so which means so