There is another type of rotations, which are called *Givens* rotations.
These are like Jacobi rotations, but their purpose is not to annihilate
one of the corner elements, *a*_{pp}, *a*_{qq}, *a*_{qp}, or *a*_{pq},
but instead to annihilate elements in the top row, i.e.,

and so on.

Because
and
for and ,
if *a*_{rp} and *a*_{rq} have been set to zero they
will *remain* zero. So these Givens rotations are not unlike
Householder rotations, but for normal filled matrices they are somewhat
less efficient. However, they're actually a little more lightweight
for tridiagonal matrices than Householder rotations, so we'll use
them to effect the final diagonalisation.