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Rank of a matrix

  1. Jan 30, 2010 #1
    Hi,

    Does anyone know how to prove rank(A)=rank(AT A) where A is any matrix and AT is the transposed of matrix A? I have difficulty to prove the part that nulity(A)=nulity(AT A). Any help will be appreciated.
     
  2. jcsd
  3. Jan 30, 2010 #2
    Try proving [tex]\operatorname{ker} A = \operatorname{ker} ( A^\top A)[/tex].
     
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