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NumPy: Compute the condition number of a given matrix

NumPy: Linear Algebra Exercise-9 with Solution

Write a NumPy program to compute the condition number of a given matrix.

From Wikipedia, In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input. Very frequently, one is solving the inverse problem – given {\displaystyle f(x)=y,} f(x) = y, one is solving for x, and thus the condition number of the (local) inverse must be used. In linear regression the condition number can be used as a diagnostic for multicollinearity.

Sample Solution :

Python Code :

import numpy as np
from numpy import linalg as LA
a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
print("Original matrix:")
print(a)
print("The condition number of the said matrix:")
print(LA.cond(a))

Sample Output:

Original matrix:
[[ 1  0 -1]
 [ 0  1  0]
 [ 1  0  1]]
The condition number of the said matrix:
1.41421356237

Python Code Editor:


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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