# Python â€“ scipy.linalg.expm

The expm() function of scipy.linalg package is used to compute the matrix exponential using Padé approximation. A Padé approximant is the "best" approximation of a function by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating.

## Syntax

scipy.linalg.expm(x)

where x is the input matrix to be exponentiated.

## Example 1

Let us consider the following example −

# Import the required libraries
from scipy import linalg
import numpy as np

# Define the input array
e = np.array([[100 , 5] , [78 , 36]])
print("Input Array :\n", e)

# Calculate the exponential
m = linalg.expm(e)

# Display the exponential of matrix
print("Exponential of e: \n", m)

## Output

The above program will generate the following output −

Input Array :
[[100 5]
[ 78 36]]
Exponential of e:
[[6.74928440e+45 4.84840154e+44]
[7.56350640e+45 5.43330432e+44]]

## Example 2

Let us take another example −

# Import the required libraries
from scipy import linalg
import numpy as np

# Define the input array
k = np.zeros((3, 3))
print("Input Array :\n", k)

# Calculate the exponential
n = linalg.expm(k)

# Display the exponential of matrix
print("Exponential of k: \n", n)

## Output

It will generate the following output −

Input Array :
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
Exponential of k:
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]

Updated on: 24-Dec-2021

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