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What are Idempotents?

  1. May 4, 2010 #1
    First what are Idempotents?
    Second, If A and B are simliar matrices, show that if A is idempotent then so is B.
     
  2. jcsd
  3. May 5, 2010 #2

    Landau

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    Re: idempotent

    First, any definition can be found on the internet. An idempotent is an 'element' a such that a^2=a. So an idempotent matrix is a matrix A such that [itex]A^2=A[/itex].

    Second, what have you tried?
     
  4. May 5, 2010 #3
    Re: idempotent

    A= A^2 then B=B^2
    A^2 = B^2 then (AB)^2 = AABB = A^2B^2 = A = b
    REALLY NOT SURE - NOT CONFIDENT IN MY THOUGHTS
     
  5. May 5, 2010 #4

    Landau

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    Re: idempotent

    This is what you need to prove.
    You can't assume that A^2=B^2. Moreover (AB)^2=ABAB, which is not the same as AABB.

    The assumption is that A and B are similar. So first you have to know what that means. If you don't, look up the definition.
     
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