ABSTRACT
The previous chapter used plane rotations multiplying a matrix from the right to orthogonalise its columns. By the essential symmetry of the singular-value decomposition, there is nothing to stop us multiplying a matrix by plane rotations from the left to achieve an orthogonalisation of its rows. The amount of work involved is of order m 2 n operations per sweep compared to mn 2 for the columnwise orthogonalisation (A is m by n), and as there are normally more rows than columns it may seem unprofitable to do this. However, by a judicious combination of row orthogonalisation with Givens’ reduction, an algorithm can be devised which will handle a theoretically unlimited number of rows.
