NumPy - Linear Algebra

The NumPy package contains a number of functions which provides all the functionality required for linear algebra. Below mentioned are the most frequently used functions to perform different algebraic calculations.

Lets discuss these functions in detail:

numpy.dot() function

The numpy.dot() function is used to return the dot product of two arrays. In the below example, dot product of Arr1 and Arr2 is calculated.

import numpy as np
Arr1 = np.array([[1, 2], 
                 [3, 4]])
Arr2 = np.array([[10, 20], 
                 [30, 40]])
Arr3 = np.dot(Arr1, Arr2)

print(Arr3)

The output of the above code will be:

[[ 70 100]
 [150 220]]

The dot product is calculated as:

[[1*10+2*30 1*20+2*40]
 [3*10+4*30 3*20+4*40]]

= [[ 70 100]
   [150 220]]

numpy.vdot() function

The numpy.vdot() function is used to return the dot product of two vectors. In the below example, dot product of vec1 and vec2 is calculated.

import numpy as np
vec1 = np.array([1, 2, 3])
vec2 = np.array([10, 20, 30])
retval = np.dot(vec1, vec2)

print(retval)

The output of the above code will be:

140

The dot product is calculated as:

1*10+2*20+3*30 = 140

numpy.inner() function

The numpy.inner() function is used to return the inner product of two arrays. In the below example, inner product of Arr1 and Arr2 is calculated.

import numpy as np
Arr1 = np.array([[1, 2], 
                 [3, 4]])
Arr2 = np.array([[10, 20], 
                 [30, 40]])
Arr3 = np.inner(Arr1, Arr2)

print(Arr3)

The output of the above code will be:

[[ 50 110]
 [110 250]]

The inner product is calculated as:

[[1*10+2*20 1*30+2*40]
 [3*10+4*20 3*30+4*40]]

= [[ 50 110]
   [110 250]]

numpy.matmul() function

The numpy.matmul() function is used to calculate the matrix multiplication of two arrays. In the below example, matrix multiplication of Arr1 and Arr2 is calculated.

import numpy as np
Arr1 = np.array([[1, 2], 
                 [3, 4]])
Arr2 = np.array([[10, 20], 
                 [30, 40]])
Arr3 = np.matmul(Arr1, Arr2)

print(Arr3)

The output of the above code will be:

[[ 70 100]
 [150 220]]

The matrix multiplication is calculated as:

[[1*10+2*30 1*20+2*40]
 [3*10+4*30 3*20+4*40]]

= [[ 70 100]
   [150 220]]

numpy.linalg.det() function

The numpy.linalg.det() function is used to calculate determinant of a matrix. In the below example, determinant of matrix mat is calculated.

import numpy as np
mat = np.array([[1, 2], 
                 [3, 4]])
retval = np.linalg.det(mat)

print(retval)

The output of the above code will be:

-2.0

The determinant is calculated as:

1*4-2*3 = -2

numpy.linalg.solve() function

The numpy.linalg.solve() function is used to solve the linear matrix equation. Consider the below mentioned system of linear equations:

Which can be represented as below in the matrix form.

The solution of the above equations is: x=1, y=5, z=7. This can be solved using numpy.linalg.solve() function as shown in below example.

import numpy as np
A = np.array([[1, 2, 3], 
              [2, 3, 1],
              [3, 1, 2]])
B = np.array([32, 24, 22])

sol = np.linalg.solve(A, B)
print(sol)

The output of the above code will be:

[ 1.  5.  7.]

numpy.linalg.inv() function

The numpy.linalg.inv() function is used to calculate the multiplicative inverse of the given matrix. In the below example, multiplicative inverse of matrix mat is calculated.

import numpy as np
mat = np.array([[1, 2], 
                [3, 4]])
invmat = np.linalg.inv(mat)

print("Original matrix:")
print(mat)

print("\nInverse matrix:")
print(invmat)

The output of the above code will be:

Original matrix:
[[1 2]
 [3 4]]

Inverse matrix:
[[-2.   1. ]
 [ 1.5 -0.5]]