Which columns are linearly independent in a matrix?

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juan 2011-9-10

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编辑： Dave Stanley 2017-8-24

Hi everybody:

I need to know what columns of a matrix are linearly independent.

Someone says that the "rref" command can do this, but I cannot get it, because I know that this command only give me a reduced form of an Echelon matrix.

What I need is the index of the columns of a matrix that are linearly independent. Can someone give me a help?

Thanks in advance.

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Answer 1

Andrei Bobrov 2011-9-10

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在 MATLAB Online 中打开

[i1 j1] = find(triu(squeeze(all(abs(diff(bsxfun(@rdivide,A,permute(A,[1 3 2]))))<1000*eps)),1));
indclm = find(~ismember(1:size(A,1),unique([i1; j1])));

variant 2

ic = nchoosek(1:size(A,2),2)
indclm = find(~ismember(1:size(A,1),unique(ic(all(abs(diff(A(:,ic(:,1))./A(:,ic(:,2)))) < 100*eps),:))))

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Answer 2

Dave Stanley 2017-8-24

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编辑：Dave Stanley 2017-8-24

I wrote a few functions to handle this. They do basically the same as Andrei's solution above, with some added bells and whistles. (Namely, it includes an option for ignoring columns that are shifted by a constant; for example, if col2 = 10 - col1 ). Hope it's useful.

For numerical matrices: https://www.mathworks.com/matlabcentral/fileexchange/64221-getlinearindependent-a-ignore-constant-shift-

For cell arrays: https://www.mathworks.com/matlabcentral/fileexchange/64222-getlinearindependentcell-a-ignore-constant-shift-