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]])])]
