I want to show that a Householder matrix is symmetric, so I must show that $H^T = H$, but from the formula
$$H= I - (uu^T/\beta),$$
they are not equal. What's wrong with my reasoning?
EDIT: I forgot that $(uu^T)^T$ would be $(u^T)^T(u)^T$ from the following properties: $(AB)^T=B^TA^T$