Let us summarise what we have learnt about Jacobi and Householder rotations.

Jacobi rotations are designed to annihilate a selected off-diagonal
element, say, *a*_{pq}. Given matrix elements *a*_{qq}, *a*_{pp},
and *a*_{pq} the rotation itself can be calculated as follows:

Householder rotations are designed to rotate the whole
under diagonal column or the whole right-to-diagonal row
onto its first direction. Given a subdiagonal column:

the rotation itself can be calculated as follows: