NumPy: Generate inner, outer, and cross products of matrices and vectors
Write a NumPy program to generate inner, outer, and cross products of matrices and vectors.
Sample Solution:
Python Code:
# Importing the NumPy library
import numpy as np
# Creating NumPy arrays 'x' and 'y'
x = np.array([1, 4, 0], float)
y = np.array([2, 2, 1], float)
# Displaying matrices and vectors 'x' and 'y'
print("Matrices and vectors.")
print("x:")
print(x)
print("y:")
print(y)
# Computing the inner product of vectors 'x' and 'y'
print("Inner product of x and y:")
print(np.inner(x, y))
# Computing the outer product of vectors 'x' and 'y'
print("Outer product of x and y:")
print(np.outer(x, y))
# Computing the cross product of vectors 'x' and 'y'
print("Cross product of x and y:")
print(np.cross(x, y))
Sample Output:
Matrices and vectors. x: [ 1. 4. 0.] y: [ 2. 2. 1.] Inner product of x and y: 10.0 Outer product of x and y: [[ 2. 2. 1.] [ 8. 8. 4.] [ 0. 0. 0.]] Cross product of x and y: [ 4. -1. -6.]
Explanation:
np.inner(x, y) computes the inner product of two arrays. For 1-D arrays, it is the sum of the product of the corresponding elements. For higher dimensions, it is a sum product over the last axes.In the given code, x and y are 1-D arrays, and the output is the sum of the element-wise product of x and y, which is 10.
np.outer(x, y) computes the outer product of two arrays. For 1-D arrays, it returns the matrix of all possible products of the elements of x and the elements of y.In the given code, x and y are 1-D arrays, and the output is a 2-D array where each element is the product of the corresponding elements of x and y.
np.cross(x, y) computes the cross product of two arrays in a 3-dimensional space. The cross product of two 1-D arrays returns a vector perpendicular to both input vectors. In the given code, x and y are 1-D arrays, and the output is the cross product of x and y, which is a 1-D array [ 4., -1., -6.]. Since the input vectors are in a 3-dimensional space, the cross product is computed using the right-hand rule.
Python-Numpy Code Editor: