Gram-Schmidt or Householder: Losing the Right Angles

Three columns that point almost the same way: a badly conditioned matrix. Each algorithm turns them into an orthonormal Q, and we run all three for real, in single precision.

In exact arithmetic classical Gram Schmidt, modified Gram Schmidt and Householder give the same Q. The three triads on the right would be identical right angles.

The rest of the narration is in the book's Companion.