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Proving Rank(A^T) = Rank (A)

  1. Oct 2, 2007 #1
    Hi, I'm new to the forum but have watched it for some time. I am trying to prove that Rank (A^T) = Rank (A) with A being mxn matrix. I suspect that it has to do with Rank (A) = Row Rank (A) = Column Rank (A) -and- A^T simply being rows / columns transposed but am unsure how to prove. Thanks, John.
  2. jcsd
  3. Oct 3, 2007 #2


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    What's the column rank of A? And what's the row rank of A^t?

    What's the relation between these two?
  4. Oct 3, 2007 #3
    They're equal !

    Col Rank (A) = Row Rank (A^T) so dim (A) = Col Rank (A) = Row Rank (A^T) = Rank (A^T). Thanks ! John.
  5. Oct 4, 2007 #4


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    use row reduction. or the general theory of dimension.
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