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Similar matrices

  1. Nov 19, 2007 #1
    can anyone guide me through this proof?

    prove that if A is idempotent and B is similar to A, then B is idempotent.(Idempotent A=A^2)
     
  2. jcsd
  3. Nov 19, 2007 #2
    So, let's think about this. If B is similar to A, then what? For some invertible matrix (of appropriate dimensions) we have:

    [tex] A [/tex] = [tex] P^{-1} [/tex] [tex] *B*P [/tex].

    Consider what [tex] A^2 [/tex] is and remember [tex] A [/tex] = [tex] A^2 [/tex].
     
    Last edited: Nov 19, 2007
  4. Nov 20, 2007 #3
    Hi everyone,

    Could someone please help me with similar proofs about similar matrices?

    -Show that if the square matrix B is similar to the square matrix A...

    -then B^k is similar to A^k for any positive integer k
    -if A is invertible, then B is invretible and B^-1 is similar to A^-1

    Thank you so much!!
     
  5. Nov 20, 2007 #4

    matt grime

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    What are the definitions (read post 2). It all follows from them directly.
     
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