For a linear mapping F, how do I define F^2?

[stgermaine]

Hi. This is a homework question, so I can't ask or give out too much info.

SO, there is a linear mapping F, and it is given that F=F^2.

Can I assume that everything about F, i.e. dimension, kernel, image, etc, is exactly the same for F^2? Or does it just mean that given a vector v, F(v) = F(F(v))?

Thank you

 

[Dick]

Hi. This is a homework question, so I can't ask or give out too much info.

SO, there is a linear mapping F, and it is given that F=F^2.

Can I assume that everything about F, i.e. dimension, kernel, image, etc, is exactly the same for F^2? Or does it just mean that given a vector v, F(v) = F(F(v))?

Thank you

It means F(v)=F(F(v)).

 

[tiny-tim]

hi stgermaine!

if F = F², F is called a projection

think how an "ordinary" projection, say from 3D to a plane or a line, works