Python sympy | Matrix.nullspace() method

With the help of sympy.Matrix().nullspace() method, we can find the Nullspace of a Matrix. Matrix().nullspace() returns a list of column vectors that span the nullspace of the matrix.

Syntax: Matrix().nullspace()

Returns: Returns a list of column vectors that span the nullspace of the matrix.

Example #1:

# import sympy
from sympy import *

M = Matrix([[1, 0, 1, 3], [2, 3, 4, 7], [-1, -3, -3, -4]])
print("Matrix : {} ".format(M))

# Use sympy.nullspace() method
M_nullspace = M.nullspace()

print("Nullspace of a matrix : {}".format(M_nullspace))

Output:

Matrix : Matrix([[1, 0, 1, 3], [2, 3, 4, 7], [-1, -3, -3, -4]]) 
Nullspace of a matrix : [Matrix([
[  -1],
[-2/3],
[   1],
[   0]]), Matrix([
[  -3],
[-1/3],
[   0],
[   1]])]

Example #2:

# import sympy
from sympy import *

M = Matrix([[14, 0, 11, 3], [22, 23, 4, 7], [-12, -34, -3, -4]])
print("Matrix : {} ".format(M))

# Use sympy.nullspace() method
M_nullspace = M.nullspace()

print("Nullspace of a matrix : {}".format(M_nullspace))

Output:

Matrix : Matrix([[14, 0, 11, 3], [22, 23, 4, 7], [-12, -34, -3, -4]]) 
Nullspace of a matrix : [Matrix([
[-1405/4254],
[   -10/709],
[  314/2127],
[         1]])]