Diagonalizable endomorphism has trivial null space

[Daaavde]

Is it correct to state that a diagonalizable endomorphism has always kernel = {0}?

 

[R136a1]

Is the zero operator a diagonalizable endomorphism?

 

[Daaavde]

I still don't understand.

 

[jgens]

R13's point was that the zero map is diagonalizable and has kernel the whole space.

 

[Daaavde]

Right, that's the case of the zero operator. But what if my eigenvalues are all non-zero (hence my eigenvectors are all linear indipendent)?

 

[jgens]

In that case your operator has trivial kernel.

 

[Daaavde]

Perfect. Thank you.