## Linear Independent Rows and Columns Generator

version 20.12.2 (5.69 KB) by
Algorithm that finds linear independent rows and columns of a matrix A. It can be found a nonsingular submatrix of A.

Updated 30 Nov 2020

From GitHub

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;

### Cite As

Gabriel Ponte (2021). Linear Independent Rows and Columns Generator (https://github.com/GabrielPonte/nsub/releases/tag/20.12.2), GitHub. Retrieved .

Marcia Fampa, Jon Lee, Gabriel Ponte, and Luze Xu. Experimental analysis of local search for sparse reflexive generalized inverses. https://https://arxiv.org/abs/2001.03732v1, 2019.

##### MATLAB Release Compatibility
Created with R2016a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux