Liquidoracid
New member
- Joined
- Sep 11, 2013
- Messages
- 3
Hello everyone 
Here's my problem :
I have a projection called p
q is defined as : q=id-p (so q is also a projection)
f is an endomorphism defined as : f=a*p+b*q (with a and b two real numbers)
I have to express fn when n is a positive or negative integer
I find, thanks to an easy induction, that if n is a positive integer : fn=an*p+bn*q
But I have no idea how to prove when n is a negative integer ? I thought about proving it's a bijection or something ?
Thanks for your help, and for your time
Here's my problem :
I have a projection called p
q is defined as : q=id-p (so q is also a projection)
f is an endomorphism defined as : f=a*p+b*q (with a and b two real numbers)
I have to express fn when n is a positive or negative integer
I find, thanks to an easy induction, that if n is a positive integer : fn=an*p+bn*q
But I have no idea how to prove when n is a negative integer ? I thought about proving it's a bijection or something ?
Thanks for your help, and for your time