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

hamza
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2022-05-18
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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.

Python programming,
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hamza
2022-05-18
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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

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