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evilpostingmong
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Homework Statement
Let T:V--->V be an operator satisfying T^2=cT c=/=0.
Show that V=U[tex]\oplus[/tex]kerT U={u l T(u)=cu}
Homework Equations
The Attempt at a Solution
Now before I start, just one quick question about ker T:
U seems to be an eigenspace since T(u)=cu with c the eigenvalue.
But that must mean that the kernel has 0 as the only element since
0 is not an eigenvector so it can't be in the eigenspace, right?
And, since T^2=cT, c cannot be 0 otherwise we would have T(0).