How to find linearly independent rows from a matrix

Question

How to identify the linearly independent rows from a matrix? For instance,

Answer 1

With sympy you can find the linear independant rows using: sympy.Matrix.rref:

>>> import sympy 
>>> import numpy as np
>>> mat = np.array([[0,1,0,0],[0,0,1,0],[0,1,1,0],[1,0,0,1]])  # your matrix
>>> _, inds = sympy.Matrix(mat).T.rref()   # to check the rows you need to transpose!
>>> inds
[0, 1, 3]

Which basically tells you the rows 0, 1 and 3 are linear independant while row 2 isn't (it's a linear combination of row 0 and 1).

Then you could remove these rows with slicing:

>>> mat[inds]
array([[0, 1, 0, 0],
       [0, 0, 1, 0],
       [1, 0, 0, 1]])

This also works well for rectangular (not only for quadratic) matrices.