# How to quickly find the minimal number of rows in a sparse matrix to form a full-rank sub-matrix?

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Benson Gou on 19 Mar 2020
Answered: Devineni Aslesha on 23 Mar 2020
Dear All,
I have a big sparse matrix A. For a given row, is it possible for me to find the minimal number of rows in A to form a full-rank sub-matrix (zero columns are deleted if zero-columns exist)?
For example, A = [0 0 1 0 3;0 2 6 0 0;1 0 5 3 1;0 2 1 4 0;-4 0 0 5 1;3 0 0 0 0;5 0 0 2 0;0 1 0 3 4].
1). For the given row #7, row #6 can form a sub-matrix with row #7.
rows_6_7 = [3 0 0 0 0;5 0 0 2 0]. Delet the zero columns, we have submatrix = [3 0; 5 2].
2). Given row #2, we can find 4 rows to form a full-rank submatrix. selected_rows = [0 2 6 0 0;0 2 1 4 0;0 1 0 3 4;0 0 1 0 3]. Submatrix = [2 6 0 0;2 1 4 0;1 0 3 4;0 1 0 3].
Thanks a lot.
Benson

Devineni Aslesha on 23 Mar 2020
Here is a similar question for your reference to find the minimal number of rows in a sparse matrix to form a full-rank sub-matrix.

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