Householder rotation.
| v | A column vector to be rotated to a multiple of the first canonical basis vector. |
| return value | The vector that generates this rotation. |
For a vector v, there is a rotation S of the form I-ww', where w is a column vector, such that the whole rotated vector Sv, except the first element, is zero. The function returns w.
v = [1;2;3;4]
w = householder(v)
(eye(numRows(v)) - w*w')*v