The Gram-Schmidt algorithm for unknown n?

Hiya,

I’m trying to understand how to carry out the gram Schmidt algorithm when you have an unknown number of vectors n.

Any help would be appreciated.

Answer 1

[David Hill]

V is matrix input where vectors are column vectors. Output U is matrix with replacement vectors as column vectors.

n = size(V,1);
k = size(V,2);
U = zeros(n,k);
U(:,1) = V(:,1)/sqrt(V(:,1)'*V(:,1));
for i = 2:k
    U(:,i) = V(:,i);
    for j = 1:i-1
        U(:,i) = U(:,i) - ( U(:,j)'*U(:,i) )/( U(:,j)'*U(:,j) )*U(:,j);
    end
    U(:,i) = U(:,i)/sqrt(U(:,i)'*U(:,i));
end

[Kai Whelan]

When I run this code for the output U I don’t get the correct values for the first column ?

[David Hill]

I believe it is correct. Do you have an example showing it does not work?

[Kai Whelan]

All good now thanks.

[ahmadreza hormozi]

nice job , thanks