How can I create this orthogonal matrix using MATLAB?

I would like to create the following matrix for know m and n.

The matrix is in the following format for 1<=j<=n. Thanks.

[Youssef Khmou]

hi, Can you mention the source of the orthogonal matrix above?

The other question is if m=n, what can you say about Lnn?

[John D'Errico]

Why would a loop not suffice?

Answer 1

[Andrew Sykes]

If m>n the following should work.

m=8;
n=5;

L=zeros(m,n);
for j=1:n
    L(:,j)=((m-n+j-1).*(m-n+j)).^(-1/2).*[ones(m-n+j-1,1) ; -(m-n+j-1) ; zeros(n-j,1)];
end
disp(L)

If m<=n, a similar approach should be possible (but this exact code will generate errors).

[Youssef Khmou]

 if m=n, the first column contains NaNs....

Answer 2

[Zeynep Erdogan]

grareg