MATLAB: How to get only linearly independent rows in a matrix or to remove linear dependency b/w rows in a matrix

linearly independentmatrixrank

Say I have a matrix A = [1,1,1;1,2,3;4,4,4]; and I want only the linearly independent rows in my new matrix. The answer might be A_new = [1,1,1;1,2,3] or A_new = [1,2,3;4,4,4]
Since I have a very large matrix so I need to decompose the matrix into smaller linearly independent full rank matrix. Can someone please help?

Best Answer

This extracts linearly independent columns, but you can just pre-transpose the matrix to effectively work on the rows.
function [Xsub,idx]=licols(X,tol)
%Extract a linearly independent set of columns of a given matrix X
%




%    [Xsub,idx]=licols(X)
%
%in:
%
%  X: The given input matrix
%  tol: A rank estimation tolerance. Default=1e-10
%
%out:
%
% Xsub: The extracted columns of X
% idx:  The indices (into X) of the extracted columns
     if ~nnz(X) %X has no non-zeros and hence no independent columns
         Xsub=[]; idx=[];
         return
     end
     if nargin<2, tol=1e-10; end
       [Q, R, E] = qr(X,0); 
       if ~isvector(R)
        diagr = abs(diag(R));
       else
        diagr = R(1);   
       end
       %Rank estimation
       r = find(diagr >= tol*diagr(1), 1, 'last'); %rank estimation
       idx=sort(E(1:r));
       Xsub=X(:,idx);
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