In the original algorithm of 1846 Jacobi would search the whole upper
triangle of matrix
**A**' and set the *largest* element
to zero. But computers are incapable of finding the largest element
simply by glancing at the whole matrix, the way we do. They can only
do things like that by looking at each element in separation from
others.

Computers are woefully shortsighted.

In our case we'll annihilate elements in a strict order by proceeding
down the rows:
**P**_{12},
**P**_{13},
**P**_{14} and so on, then
**P**_{23},
**P**_{24}, etc. One such set of *n*(*n*-1)/2 Jacobi
rotations is called a *sweep*.