(4) Page 76, Problem 10.2.
10.2. (a) Write a MATLAB function [W,R] = house(A) that computes an
implicit representation of a full QR factorization A = QR of an m X n matrix
A with m > n using Householder reflections. The output variables are a
lower-triangular matrix W € Cmxn whose columns are the vectors Uk defining
the successive Householder reflections, and a triangular matrix R € C71,71
(b) Write a MATLAB function Q = formQ(W) that takes the matrix W pro-
duced by house as input and generates a corresponding m X m orthogonal
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% test Housholder
m = 9;
n = 5;
A = rand(m,n);
% factorize and check errors
[W,R] = house(A);
Q = formQ(W);
maxError = max(max(abs(Q*R-A)))
% Compare with Matlab
[Qm,Rm] = qr(A);
diffRml = max(max(abs(R-Rm)))
diffQml = max(max(abs(Q-Qm)))