Let us summarise what we have learnt about Jacobi and Householder rotations.
Jacobi rotations are designed to annihilate a selected off-diagonal
element, say, apq. Given matrix elements aqq, app,
and apq 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: