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Normal matrices

  1. Aug 10, 2010 #1
    Hello,

    can you help me with the proof? If A is normal
    [tex]A^TA=AA^T[/tex]
    then A and A^T have the same nullspace (kernel). And
    [tex]||Ax||=||A^Tx||[/tex]

    Thank you.
     
  2. jcsd
  3. Aug 10, 2010 #2
    [itex] A^TAx = 0 = AA^Tx [/itex] for the vectors in the nullspace right?
     
  4. Aug 10, 2010 #3
    don't understand your hint.
     
  5. Aug 10, 2010 #4
    multiply both by [itex]x^T[/itex] from the left, what is the resulting expression in terms of norms?
     
  6. Aug 11, 2010 #5
    yes, I understand, thank you
     
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