Exercise 3.4.1
Find a Householder reflector P such that
P[29−6]=[1100].
z = [2,9,-6];
FNC.norm(z)
# 11.0
This is of the form that we can apply Theorem 3.4.2.
e1 = [1,0,0];
w = FNC.norm(z)*e1 - z;
v = w/FNC.norm(w);
P = I - 2*v*v';
# verify
P*z
#3-element Vector{Float64}:
# 11.0
# -8.881784197001252e-16
# 8.881784197001252e-16