NumPy: Compute the eigenvalues and right eigenvectors of a given square array

NumPy: Linear Algebra Exercise-7 with Solution

Write a NumPy program to compute the eigenvalues and right eigenvectors of a given square array.

Sample Solution :

Python Code :

import numpy as np
m = np.mat("3 -2;1 0")
print("Original matrix:")
print("a\n", m)
w, v = np.linalg.eig(m) 
print( "Eigenvalues of the said matrix",w)
print( "Eigenvectors of the said matrix",v)

Sample Output:

Original matrix:
 [[ 3 -2]
 [ 1  0]]
Eigenvalues of the said matrix [ 2.  1.]
Eigenvectors of the said matrix [[ 0.89442719  0.70710678]
 [ 0.4472136   0.70710678]]

Python Code Editor:

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Previous: Write a NumPy program to compute the inner product of vectors for 1-D arrays (without complex conjugation) and in higher dimension.
Next: Write a NumPy program to compute the Kronecker product of two given mulitdimension arrays.

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Python: Tips of the Day

Getting the last element of a list:

some_list[-1] is the shortest and most Pythonic.

In fact, you can do much more with this syntax. The some_list[-n] syntax gets the nth-to-last element. So some_list[-1] gets the last element, some_list[-2] gets the second to last, etc, all the way down to some_list[-len(some_list)], which gives you the first element.

You can also set list elements in this way. For instance:

>>> some_list = [1, 2, 3]
>>> some_list[-1] = 5 # Set the last element
>>> some_list[-2] = 3 # Set the second to last element
>>> some_list
[1, 3, 5]

Note that getting a list item by index will raise an IndexError if the expected item doesn't exist. This means that some_list[-1] will raise an exception if some_list is empty, because an empty list can't have a last element.

Ref: https://bit.ly/3d8TfFP