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Unitary matrix question

  1. Jun 17, 2011 #1

    td21

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    "orthonormal columns imply orthonormal rows for square matrix."

    My proof is:
    [itex]Q^{T}Q=I[/itex](orthonormal columns)
    implys
    [itex]QQ^{T}=I[/itex](orthonoraml rows)

    for square matrix.


    But i think this proof is kind of indirect. Is there another more direct proof from the definition of inner product or norm?
     
  2. jcsd
  3. Jun 18, 2011 #2

    Fredrik

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    I think that's as direct and simple as it gets. I would only add the explanation of how [itex]Q^TQ=I[/itex] implies [itex]QQ^T=I[/itex].
     
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