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Homework Help: Linear Algebra- Diagonal Matrix

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Let D be an n x n diagonal matrix whose diagonal entries are either 0 or 1

    a) Show that D is idempotent

    b) Show that if X is a nonsingular matrix and A=XD(X)-1 , then A is idempotent


    2. Relevant equations



    3. The attempt at a solution

    a) I tried it, and it works for a specific matrix, say 3x3... but I don't know if it's really a proof.
    I need to show that

    D2=D

    b) I solved this part

    Also,
    is (AB)2= A2*B2
    or
    (AB)2=B2*A2
    ?
     
    Last edited: Mar 6, 2010
  2. jcsd
  3. Mar 6, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You just need to make up some notation. Let diag(a1,a2,...an) be the matrix whose diagonal entries are a1, a2... Now what diag(a1,a2,...an)*diag(b1,b2,...bn)? (AB)^2 generally isn't equal to either A^2*B^2 or B^2*A^2. It's just ABAB.
     
  4. Mar 6, 2010 #3
    oh, right , it works ...
    thanks a lot for the help ....
     
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