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

Question

Benson Gou 2020-3-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/511796-how-to-quickly-find-the-minimal-number-of-rows-in-a-sparse-matrix-to-form-a-full-rank-sub-matrix

回答： Devineni Aslesha 2020-3-23

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