The second and the third equations of (2) are similar to the first, except that the bases of the coefficients b are different and postmultiplication
of x and [x.sup.2] should be processed.
Of course, the choice of G is unique only up to postmultiplication
by an orthogonal matrix.
Consequently, postmultiplication with [Mathematical Expression Omitted] leaves the first n + k - 1 columns of [Mathematical Expression Omitted] unaltered.
Since postmultiplication with any [Q.sup.<n>] does not affect the first n columns, clearly the reflection vectors of the first [[Mu].sub.2] - 1 Householder reflections of [A.sub.b+1] (the ones involved in the computation of [A.sub.11]) are the reflection vectors of the first [[Mu].sub.2] - 1 Householder reflections of [A.sub.1] augmented with zeros.
(S W) is a sort of left quotient of W by S; the divisor S can be canceled by postmultiplication
, and the result will be the same as W or better.