Python sympy | Matrix.eigenvects() method

With the help of sympy.Matrix().eigenvects() method, we can find the Eigenvectors of a matrix. eigenvects() method returns a list of tuples of the form (eigenvalue:algebraic multiplicity, [eigenvectors]).

Syntax: Matrix().eigenvects()

Returns: Returns a list of tuples of the form (eigenvalue:algebraic multiplicity, [eigenvectors]).

Example #1:

# import sympy
from sympy import * M = Matrix([[3, -2,  4, -2],
                                [5,  3, -3, -2],
                                [5, -2,  2, -2],
                                [5, -2, -3,  3]])

print("Matrix : {} ".format(M))

# Use sympy.eigenvects() method
M_eigenvects = M.eigenvects()

print("Eigenvects of a matrix : {}".format(M_eigenvects))

Output:

Matrix : Matrix([[3, -2, 4, -2], [5, 3, -3, -2], [5, -2, 2, -2], [5, -2, -3, 3]])
Eigenvects of a matrix : [(-2, 1, [Matrix([
[0],
[1],
[1],
[1]])]), (3, 1, [Matrix([
[1],
[1],
[1],
[1]])]), (5, 2, [Matrix([
[1],
[1],
[1],
[0]]), Matrix([
[ 0],
[-1],
[ 0],
[ 1]])])]

Example #2:

# import sympy
from sympy import * M = Matrix([[1, -3, 3], [3, -5, 3], [6, -6, 4]])
print("Matrix : {} ".format(M))

# Use sympy.eigenvects() method
M_eigenvects = M.eigenvects()

print("Eigenvects of a matrix : {}".format(M_eigenvects))

Output:

Matrix : Matrix([[1, -3, 3], [3, -5, 3], [6, -6, 4]])
Eigenvects of a matrix : [(-2, 2, [Matrix([
[1],
[1],
[0]]), Matrix([
[-1],
[ 0],
[ 1]])]), (4, 1, [Matrix([
[1/2],
[1/2],
[ 1]])])]