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, app, aqq, aqp, or apq,
but instead to annihilate elements in the top row, i.e.,
Because and for and , if arp and arq 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.