1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Diagonal matrix

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Suppose the matrix A , B are diagonalizable and have the same eigenvectors. Show AB=BA

    2. Relevant equations

    3. The attempt at a solution

    There exists a matrix P s.t. (P^-1)AP=(P^-1)BP

    I played around with this, and could not get anywhere..
  2. jcsd
  3. Oct 11, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    If A is diagonalizable then there is a basis where it's a diagonal matrix. Then all of the basis vectors are eigenvectors. If B has the same eigenvectors then it's also a diagonal matrix in the same basis. Now you just have to show two diagonal matrices commute.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Diagonal matrix
  1. Diagonalizing a matrix (Replies: 3)

  2. Diagonalize a matrix (Replies: 3)

  3. Diagonalizing a matrix (Replies: 1)