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Linear Algebra- Diagonal Matrix

  • Thread starter Roni1985
  • Start date
  • #1
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Homework Statement



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


Homework Equations





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:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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.
 
  • #3
201
0
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.
oh, right , it works ...
thanks a lot for the help ....
 

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