1. ## Imf=Kerf

May you help me please, with an example of a vector space V and a linear mapping f:V->V , such that Imf=Kerf?

2. ## Re: Imf=Kerf

Originally Posted by jojo7777777
May you help me please, with an example of a vector space V and a linear mapping f:V->V , such that Imf=Kerf?
For example, $f:\mathbb{R}^2\to \mathbb{R}^2$ defined by $f(x_1,x_2)=(0,x_1)$.