Page "Orthogonal matrix" Paragraph 79

Likewise, algorithms using Householder and Givens matrices typically use specialized methods of multiplication and storage.

For example, a Givens rotation affects only two rows of a matrix it multiplies, changing a full multiplication of order n < sup > 3 </ sup > to a much more efficient order n. When uses of these reflections and rotations introduce zeros in a matrix, the space vacated is enough to store sufficient data to reproduce the transform, and to do so robustly.

( Following, we do not store a rotation angle, which is both expensive and badly behaved.