# Unitary matrix question

1. Jun 17, 2011

### td21

"orthonormal columns imply orthonormal rows for square matrix."

My proof is:
$Q^{T}Q=I$(orthonormal columns)
implys
$QQ^{T}=I$(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. Jun 18, 2011

### Fredrik

Staff Emeritus
I think that's as direct and simple as it gets. I would only add the explanation of how $Q^TQ=I$ implies $QQ^T=I$.