In Python, we can use the outer() function of the NumPy package to find the outer product of two matrices.
Syntax : numpy.outer(a, b, out = None)
Parameters :
a : [array_like] First input vector. Input is flattened if not already 1-dimensional.
b : [array_like] Second input vector. Input is flattened if not already 1-dimensional.
out : [ndarray, optional] A location where the result is stored.
Return : [ndarray] Returns the outer product of two vectors. out[i, j] = a[i] * b[j]
Example 1: Outer Product of 1-D array
Python3
# Importing libraryimport numpy as np# Creating two 1-D arraysarray1 = np.array([6,2])array2 = np.array([2,5])print("Original 1-D arrays:")print(array1)print(array2)# Outputprint("Outer Product of the two array is:")result = np.outer(array1, array2)print(result) |
Output:
Original 1-D arrays: [6 2] [2 5] Outer Product of the two array is: [[12 30] [ 4 10]]
Time Complexity: O(n^2), where n is the length of the input arrays “array1” and “array2”.
Space Complexity: O(n^2)
Example 2: Outer Product of 2X2 matrix
Python3
# Importing libraryimport numpy as np# Creating two 2-D matrixmatrix1 = np.array([[1, 3], [2, 6]])matrix2 = np.array([[0, 1], [1, 9]])print("Original 2-D matrix:")print(matrix1)print(matrix2)# Outputprint("Outer Product of the two matrix is:")result = np.outer(matrix1, matrix2)print(result) |
Output:
Original 2-D matrix: [[1 3] [2 6]] [[0 1] [1 9]] Outer Product of the two matrix is: [[ 0 1 1 9] [ 0 3 3 27] [ 0 2 2 18] [ 0 6 6 54]]
Example 3: Outer Product of 3X3 matrix
Python3
# Importing libraryimport numpy as np# Creating two 3-D matrixmatrix1 = np.array([[2, 8, 2], [3, 4, 8], [0, 2, 1]])matrix2 = np.array([[2, 1, 1], [0, 1, 0], [2, 3, 0]])print("Original 3-D matrix:")print(matrix1)print(matrix2)# Outputprint("Outer Product of the two matrix is:")result = np.outer(matrix1, matrix2)print(result) |
Output:
Original 3-D matrix: [[2 8 2] [3 4 8] [0 2 1]] [[2 1 1] [0 1 0] [2 3 0]] Outer Product of the two matrix is: [[ 4 2 2 0 2 0 4 6 0] [16 8 8 0 8 0 16 24 0] [ 4 2 2 0 2 0 4 6 0] [ 6 3 3 0 3 0 6 9 0] [ 8 4 4 0 4 0 8 12 0] [16 8 8 0 8 0 16 24 0] [ 0 0 0 0 0 0 0 0 0] [ 4 2 2 0 2 0 4 6 0] [ 2 1 1 0 1 0 2 3 0]]
