<Dd> Q T Q = Q Q T = I, (\ displaystyle Q ^ (\ mathrm (T)) Q = QQ ^ (\ mathrm (T)) = I,) </Dd> <P> where I (\ displaystyle I) is the identity matrix . </P> <P> This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: </P> <Dl> <Dd> Q T = Q − 1 . (\ displaystyle Q ^ (\ mathrm (T)) = Q ^ (- 1).) </Dd> </Dl>

When does the transpose of a matrix equal the inverse