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Math Help - Similarity matrices

  1. #1
    Junior Member
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    Similarity matrices

    Hi there. Please help me this problem. I was so worried about it. Thank you.
    Let A, B are matrices such that A^2=A,\quad  B^2=B. Prove that A, B are similar if and only if rank A= rank B.
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  2. #2
    Member Haven's Avatar
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    Re: Similarity matrices

    The forward direction is a direct application of the definition of similar. That is there is an invertible matrix U, such that
    A = (UBU^{-1})

    for the converse, consider a change of basis matrix, (is this matrix invertible and why?)
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