• Support PF! Buy your school textbooks, materials and every day products Here!

Proving diagonalizability with the power series

  • Thread starter rugbygirl2
  • Start date
  • #1

Homework Statement


If A is a diagonal matrix with the diagonal entries a1, a2, ...., an, use the power series to prove that exp(At) is a diagonal matrix with the entries exp(a1t), exp(a2t), ....., exp(ant).


Homework Equations





The Attempt at a Solution


I can prove that A is diagonalizable with T-1 AT=D, but I'm not sure how to begin the proof using the power series as a method. My book does not discuss this and any insight would be greatly appreciated, thanks!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You don't have to diagonalize A. It's already diagonal. You just have to realize that the power series of A is the same as the power series of the diagonal elements.
 

Related Threads for: Proving diagonalizability with the power series

Replies
1
Views
414
  • Last Post
Replies
3
Views
1K
Replies
29
Views
1K
Replies
3
Views
2K
Replies
2
Views
4K
Replies
2
Views
4K
Replies
3
Views
1K
Top