Hi,
I would like some help with the following problem:
Find a vector space V and a linear transformation T: V .... V such that V = N(T) + R(T) and N(T) intersection R(T) is not equal to {0}
(V cant be finite dimensional)
it's an extra credit Q please help.
Thank you.
Hmmm...V is the real vec. space of all real sequences, with addition defined by and multiplcation by scalar defined by
This is fairly well-known nice example of infinite dimensional v.s. You can also focus on the v.s. of all convergent sequences, of all convergent to zero sequences, etc.
Tonio