The Gram-Schmidt algorithm for unknown n?

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Kai Whelan 2020-4-29

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评论： ahmadreza hormozi 2021-3-18

采纳的回答： David Hill

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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采纳的回答

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