Find a matrix or vector norm using NumPy
To find a matrix or vector norm we use function numpy.linalg.norm() of Python library Numpy. This function returns one of the seven matrix norms or one of the infinite vector norms depending upon the value of its parameters.
Syntax: numpy.linalg.norm(x, ord=None, axis=None)
Parameters:
x: input
ord: order of norm
axis: None, returns either a vector or a matrix norm and if it is an integer value, it specifies the axis of x along which the vector norm will be computed
Example 1:
Python3
import numpy as np
vec = np.arange( 10 )
vec_norm = np.linalg.norm(vec)
print ( "Vector norm:" )
print (vec_norm)
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Output:
Vector norm:
16.881943016134134
The above code computes the vector norm of a vector of dimension (1, 10)
Example 2:
Python3
import numpy as np
mat = np.array([[ 1 , 2 , 3 ],
[ 4 , 5 , 6 ]])
mat_norm = np.linalg.norm(mat)
print ( "Matrix norm:" )
print (mat_norm)
|
Output:
Matrix norm:
9.539392014169456
Here, we get the matrix norm for a matrix of dimension (2, 3)
Example 3:
To compute matrix norm along a particular axis –
Python3
import numpy as np
mat = np.array([[ 1 , 2 , 3 ],
[ 4 , 5 , 6 ]])
mat_norm = np.linalg.norm(mat, axis = 1 )
print ( "Matrix norm along particular axis :" )
print (mat_norm)
|
Output:
Matrix norm along particular axis :
[3.74165739 8.77496439]
This code generates a matrix norm and the output is also a matrix of shape (1, 2)
Example 4:
Python3
import numpy as np
vec = np.arange( 9 )
mat = vec.reshape(( 3 , 3 ))
vec_norm = np.linalg.norm(vec)
print ( "Vector norm:" )
print (vec_norm)
mat_norm = np.linalg.norm(mat)
print ( "Matrix norm:" )
print (mat_norm)
|
Output:
Vector norm:
14.2828568570857
Matrix norm:
14.2828568570857
From the above output, it is clear if we convert a vector into a matrix, or if both have same elements then their norm will be equal too.
Last Updated :
06 Jun, 2021
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