unitary matrix question

td21

"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?

Fredrik

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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td21	unitary matrix question Tweet "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?

Fredrik Mentor	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].