QR Factorization using Householder Transformation

Hello!

I am trying to compute a function householder that taking a matrix A, returns the matrix Q R such that

This is my code so far but it seems that I have a mistake since ~= A:

Any help please?

function [Q,R] = householder(A)
   % Write your code here.
   [m,n] = size(A);
    Q = A; 
    for j = 1:m
        z = Q(j:end,j);
        v = [ -sign(z(1))*norm(z)-z(1); -z(2:end)];
        
        P = eye(size(z,1), size(z,1)) - (2/(v'*v))*(v*v');
        
        Q(j:end, j:end) = P* Q(j:end, j:end);
        

    end
    
    R = Q' * A;
    
end

Answer 1

[Monisha Nalluru]

Refer to the following blog post which gives example and clear understanding on Household Refelection and Household QR factorization with sample code.