Linear Independent Rows and Columns Generator

Algorithm that finds linear independent rows and columns of a matrix A. It can be found a nonsingular submatrix of A.

nsub nonsingular submatrix

Assuming that A is an m-by-n matrix and rank(A)>=r, [R] = nsub(A,r) returns a vector R with r elements in the range (1:m), such that the rows of A(R,:) are linear independent.

[R,C] = nsub(A,r) returns a vector R with r elements in the range (1:m) and a vector C with r elements in the range (1:n), such that A(R,C) is a nonsingular submatrix of A.

Note: If r>rank(A) nsub returns an error message.

%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Example:

%

% r = 3;

% A = [-1 -1 1 1 -5; -1 -1 1 0 -5; 0 0 0 1 0; 2 1 1 1 1];

%

% Note: row3 = row1 - row2

%

% [R,C] = nsub(A,r);

%

% Result:

% R = [2 4 1];

% C = [5 1 4];

% A(R,C) = [-5 1 0; 1 2 1; -5 -1 1];

% rank(A(R,C)) = 3;