Hello /sci/,
We all know induction can be used to prove summation formulas. My question is, how do I use induction to establish a new formula?
Specifically I am trying to show that if T is a linear transformation and ||T- I|| < 1 where || * || is the linear operator norm, that the sum of ||T-I||= T^-1.
I have a solution (pic related) I just do not get the induction step. I understand everything else. Any help would be greatly appreciated.
We all know induction can be used to prove summation formulas. My question is, how do I use induction to establish a new formula?
Specifically I am trying to show that if T is a linear transformation and ||T- I|| < 1 where || * || is the linear operator norm, that the sum of ||T-I||= T^-1.
I have a solution (pic related) I just do not get the induction step. I understand everything else. Any help would be greatly appreciated.
