# 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.

Numpy Documentation

```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).

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.

1. Sinister says:
2. Vivek Dadhich says: