# How to compute eigen values and eigen vectors in Python

In this python tutorial, we will write a code in Python on how to compute eigenvalues and vectors.

### Creation of a Square Matrix in Python

First, we will create a square matrix of order 3X3 using **numpy **library.

Numpy is a Python library which provides various routines for operations on arrays such as mathematical, logical, shape manipulation and many more.

To know more about the numpy library refer the following link:

import numpy as np a=np.array([[1,2,3],[4,5,6],[7,8,9]])

To print the created matrix use the print function.

print(a)

Output:

[[1 2 3] [4 5 6] [7 8 9]]

## Computation of Eigen Values and Eigen Vectors

After creating a square matrix using **numpy** library we have to use a package in this library known as **numpy.linalg**. This library is used for calculating all the linear algebra functions like vector products matrix operations(inverse, transpose).

To know more about this library refer the following link

https://docs.scipy.org/doc/numpy-1.13.0/reference/routines.linalg.html

In this library, we have to import the function known as eig to compute eigenvalues and vectors.

from numpy.linalg import eig values , vectors = eig(a) print(values) print(vectors)

**Output 1:**

Eigenvalues

[ 1.61168440e+01 -1.11684397e+00 -1.30367773e-15]

**Output 2:**

Eigenvectors

[[-0.23197069 -0.78583024 0.40824829] [-0.52532209 -0.08675134 -0.81649658] [-0.8186735 0.61232756 0.40824829]]

Using this function and this package we can compute eigenvectors and eigenvalues for any square matrix of order nXn.

Example-2:

from numpy.linalg import eig import numpy as np a=np.array([[10,20,30,40],[1,2,3,5],[7,8,9,10],[15,25,35,45]]) values , vectors = eig(a) print(values) print(vectors)

Output 1:

Eigen Values

[ 6.96947758e+01 -3.22806629e+00 -4.66709488e-01 -3.59740472e-14]

Output 2:

Eigen Vectors

[[-6.28224280e-01 -7.67762260e-01 -5.75701703e-01 -4.08248290e-01] [-7.35387665e-02 -1.62230993e-02 7.06561093e-01 8.16496581e-01] [-2.05200662e-01 6.09975078e-01 2.05319101e-01 -4.08248290e-01] [-7.46872808e-01 -1.95469507e-01 -3.56627310e-01 -2.73218204e-14]]

The above output is an example of a square matrix of order 4X4.

You can also read,

Thank you for the information. !

how to write a python program to find the rank of a 6*6 matrix and its eigen value also ?