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Reputation: 63

How to determine two vectors are linearly dependent or independent in python?

Take in two 3 dimensional vectors, each represented as an array, and tell whether they are linearly independent. I tried to use np.linalg.solve() to get the solution of x, and tried to find whether x is trivial or nontrivial. But it shows 'LinAlgError: Last 2 dimensions of the array must be square'. Can anyone help me how to figure that out?

from sympy import *
import numpy as np
from scipy import linalg
from numpy import linalg

v1 = np.array([0, 5, 0])
v2 = np.array([0, -10, 0])
a = np.array([v1,v2])
b = np.zeros(3)
x = np.linalg.solve(a, b)

Upvotes: 1

Views: 8155

Answers (2)

Muhammad Junaid Haris
Muhammad Junaid Haris

Reputation: 452

As your final matrix will be in a rectangular form, a simple approach of EigenValues will not work. You need to use the library of sympy

import sympy 
import numpy as np
matrix = np.array([
  [0, 5, 0],
  [0, -10, 0]
])

_, indexes = sympy.Matrix(matrix).T.rref()  # T is for transpose
print(indexes)

This will print the indexes of linearly independent rows. To further print them from the matrix, use

print(matrix[indexes,:])

To answer your specific question, check if two vectors are linearly dependant or not. You can most definitely use an if statement afterwards if it is the two vectors you are always going to check.

if len(indexes) == 2:
    print("linearly independant")
else:
    print("linearly dependant")

Upvotes: 2

Vasu Makwana
Vasu Makwana

Reputation: 33

If one eigenvalue of the matrix is zero, its corresponding eigenvector is linearly dependent.

So the following code would work for simple case:

from sympy import *
import numpy as np
from scipy import linalg
from numpy import linalg

matrix = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 1, 0], [1, 0, 0,
                  1]])

(lambdas, V) = np.linalg.eig(matrix.T)
print matrix[lambdas == 0, :]

Output: [[0 1 1 0]]

Upvotes: 0

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