Linear Algebra: Practice Programs in Python and C Languages
Computation of Eigen Values and Eigen Vectors Using Python (Linear Algebra: Linear Transformation and Diagonalization)
Linear Algebra: Practice Programs in Python and C Languages: Linear Algebra: Linear Transformation and Diagonalization: Computation of Eigen Values and Eigen Vectors Using Python
Linear Algebra
PROGRAMMES
IN PYTHON AND C LANGUAGES
UNIT − II:
LINEAR TRANSFORMATION AND DIAGONALIZATION
COMPUTATION OF EIGEN
VALUES AND EIGEN VECTORS USING PYTHON
The
computation of eigenvalues and eigenvectors of a 3×3 matrix in Python can be
efficiently performed using the numpy library, specifically the
numpy.linalg.eig function.
Here's
how to do it: import numpy.
Python
import numpy as np
Define
the 3×3 Matrix.
Create
a NumPy array representing your 3×3 matrix.
Python
matrix_A = np.array([all, a12,
a13],
[a21, a22, a23]
[a31, a3a, a33]])
Replace
all, a12, etc., with the
actual numerical values of your matrix elements. Compute Eigenvalues and
Eigenvectors.
Use
the np.linalg.eig() function, which returns two values: an array of eigenvalues
and a 2D array where each column is an eigenvector.
Python
eigenvalues, eigenvectors = np.linalg.eig (matrix_A)
Display
the Results
Print
the computed eigenvalues and eigenvectors.
Python
print ("Eigenvalues of the matrix: ")
print (eigenvalues)
print ("\nEigenvectors of the matrix (columns correspond to
eigenvalues):")
print (eigenvectors)
Example
Python
import numpy as np
#Define a sample 3 x 3 matrix
matrix_B = np.array([[4,2,0],
[1,3,0];
[0,0,5]])
# Compute eigenvalues and eigenvectors
eigenvalues, eigenvectors = np.linalg.eig (matrix_B)
#Print the results
print ("Eigenvalues of the matrix:")
print (eigenvalues).
print ("\nEigenvectors of the matrix (columns correspond to
eigenvalue): ")
print (eigenvectors)
In
the output, eigenvalues will be a 1D array containing the eigenvalues.
Eigenvectors will be a 2D array where each column represents an eigenvector,
and the order of the eigenvectors corresponds to the order of the eigenvalues
in the eigenvalues array.
Linear Algebra: Practice Programs in Python and C Languages : Tag: maths, mathematics : - Computation of Eigen Values and Eigen Vectors Using Python (Linear Algebra: Linear Transformation and Diagonalization)
Linear Algebra: Practice Programs in Python and C Languages
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Linear Algebra
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