Let V=P(R), and for define , where is the jth derivative of f(x). Prove that the set is a linearly independent subset of , the vector space of all linear transformations from V into V.
I don't really know how to even start...
Let V=P(R), and for define , where is the jth derivative of f(x). Prove that the set is a linearly independent subset of , the vector space of all linear transformations from V into V.
I don't really know how to even start...
I think I just solved the problem.
I assume to the contrary that the set is linearly dependent for all f(x). Then I pick , then , but then I found , which is impossible.
Sorry, I think I posted this problem up a bit too hasty, I should have been able to solve it earlier.
Thank you!