Hey everyone, I have a question here that says the following:
Suppose that T belongs to L(C^5)[C to the fifth power] and its matrix in the standard basis is as following:
5 1 0 0 0
0 5 0 0 2
0 0 2 0 3
0 0 0 2 4
0 0 0 0 5
Find the Jordan form, the Jordan basis, and also the minimal polynomial of T.
I am having a lot of trouble with Jordan form, and after reading and re-reading the text, along with several examples I am still lost at how to approach this question. Any help is greatly appreciated, thanks everyone.