unitary matrix question


by td21
Tags: matrix, unitary
td21
td21 is offline
#1
Jun17-11, 10:36 PM
P: 74
"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?
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Fredrik
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#2
Jun18-11, 03:53 AM
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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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