Function make_householder_in_place 

pub fn make_householder_in_place<T: ComplexField>(
    head: &mut T,
    tail: ColMut<'_, T>,
) -> HouseholderInfo<T>

computes the householder reflection $I - \frac{v v^H}{\tau}$ such that when multiplied by $x$ from the left, the result is $\beta e_0$. $\tau$ and $(\text{head} - \beta)^{-1}$ are returned and $\tau$ is real-valued. $\beta$ is stored in head

$x$ is determined by $x_0$, contained in head, and $|x_{1\dots}|$, contained in tail_norm. the vector $v$ is such that $v_0 = 1$ and $v_{1\dots}$ is stored in essential (when provided)