Scientific Computing

This module demonstrates the construction of a Householder
transformation to annihilate the second component of a vector in two
dimensions. Given a vector *a*, the corresponding Householder
transformation has the form ** H** =

The user first clicks on the graph to select a vector in the plane. The user then clicks on the successive buttons to draw an appropriate mirror, project the original vector onto the mirror, and then extend the projection twice as far to reach the first coordinate axis, at which point the second coordinate is zero and the 2-norm is preserved, as required. The user can select either positive or negative sign, which determines which of the two possible mirrors and vectors will result.

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 3.5.1, especially Figure 3.3.

**Developers:** Nicholas Exner and Michael Heath