The Gram-Schmidt algorithm for unknown n?

2020 4 29
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更新时间：2021 3 18
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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.

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David Hill
David Hill 2020-4-29

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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

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Kai Whelan
Kai Whelan 2020-4-29
When I run this code for the output U I don’t get the correct values for the first column ?
David Hill
David Hill 2020-4-29
I believe it is correct. Do you have an example showing it does not work?

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