NumPy: Compute the inner product of vectors for 1-D arrays and in higher dimension

NumPy: Linear Algebra Exercise-6 with Solution

Write a NumPy program to compute the inner product of vectors for 1-D arrays (without complex conjugation) and in higher dimension.

Sample Solution:

Python Code :

import numpy as np

# Create two 1-D arrays 'a' and 'b'
a = np.array([1, 2, 5])
b = np.array([2, 1, 0])

# Display the original 1-D arrays 'a' and 'b'
print("Original 1-d arrays:")
print(a)
print(b)

# Calculate the inner product of arrays 'a' and 'b' using np.inner()
result = np.inner(a, b)

# Display the inner product of the said vectors
print("Inner product of the said vectors:")
print(result)

# Create two 3x3 arrays 'x' and 'y'
x = np.arange(9).reshape(3, 3)
y = np.arange(3, 12).reshape(3, 3)

# Display the original higher-dimensional arrays 'x' and 'y'
print("Higher dimension arrays:")
print(x)
print(y)

# Calculate the inner product of arrays 'x' and 'y' using np.inner()
result = np.inner(x, y)

# Display the inner product of the said vectors
print("Inner product of the said vectors:")
print(result) 

Sample Output:

Original 1-d arrays:
[1 2 5]
[2 1 0]
Inner product of the said vectors:
Higher dimension arrays:
[[0 1 2]
 [3 4 5]
 [6 7 8]]
[[ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
Inner product of the said vectors:
[[ 14  23  32]
 [ 50  86 122]
 [ 86 149 212]]

Explanation:

In the above code –

m = np.mat("3 -2;1 0"): This line creates a 2x2 NumPy matrix m with the elements:

[[ 3, -2],

[ 1, 0]]

w, v = np.linalg.eig(m): This line computes the eigenvalues and eigenvectors of the matrix m. The eig function takes a square matrix as input and returns two arrays: one containing the eigenvalues, and the other containing the corresponding eigenvectors as columns.

print( "Eigenvalues of the said matrix", w): This line prints the eigenvalues of the matrix m. In this case, the eigenvalues are 2.0 and 1.0.

print( "Eigenvectors of the said matrix", v): This line prints the eigenvectors of the matrix m as columns of the v array. The eigenvectors corresponding to the eigenvalues 2.0 and 1.0 are [[-0.89442719, 0.70710678], [-0.4472136 , -0.70710678]].

Python-Numpy Code Editor:

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