# Python NumPy numpy.linalg.norm() Function

Python NumPy `numpy.linalg.norm()` function finds the value of the matrix norm or the vector norm. The parameter `ord` decides whether the function will find the matrix norm or the vector norm. It has several defined values.

## Syntax of `numpy.linalg.norm()`

``````numpy.linalg.norm(x,
ord= None,
axis= None,
keepdims= False)
``````

### Parameters

`x` It is an `array`-like structure. It is the input `array` used for finding the value of the norm. The default value for the `axis` parameter is `None` so, the `array` should be one-dimensional or two-dimensional provided `ord` is `None`.
`ord` The returned value of the function depends on this parameter. It defines the order of the norm. It has several values, check here.
`axis` It is an `integer`, `None` or 2-`tuple` of integers. If it is an `integer` then it represents the axis along which the function will find the vector norm. Its default value is `None` which means that the function will find either matrix norm or vector norm. If it is a 2-`tuple` integer value then the function will return the value of matrix norm.
`keepdims` It is a `Boolean` parameter. Its default value is `False`. If its value is `True` then it shows the dimensions of the normed axis with the size equal to one.

### Return

It returns the norm of the matrix or a vector in the form of a `float` value or an N-dimensional `array`.

## Example Codes: `numpy.linalg.norm()`

We will use this function to find the norm of a one-dimensional `array`.

``````from numpy import linalg as la
import numpy as np

x = np.array([89, 34, 56, 87, 90, 23, 45, 12, 65, 78, 9, 34, 12, 11, 2, 65, 78, 82, 28, 78])

norm = la.norm(x)
print('The value of norm is:')
print(norm)
``````

Output:

``````The value of norm is:
257.4800963181426
``````

It has returned a `float` value which is the value of norm.

## Example Codes: `numpy.linalg.norm()` to Find the Norm of a Two-Dimensional Array

We will pass a two-dimensional `array` now.

``````from numpy import linalg as la
import numpy as np

x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])

norm = la.norm(x)
print('The value of norm is:')
print(norm)
``````

Output:

``````The value of norm is:
129.35223229616102
``````

If we set the `ord` parameter to any other value than `None` and pass an `array` that is neither one-dimensional nor two-dimensional, the function will generate a `ValueError` as the `axis` parameter is `None`.

``````from numpy import linalg as la
import numpy as np

x = np.array([[[4, 2], [6, 4]], [[5, 8], [7, 3]]])

norm = la.norm(x,'nuc')
print('The value of norm is:')
print(norm)
``````

Output:

``````Traceback (most recent call last):
File "C:\Test\test.py", line 6, in <module>
norm = la.norm(x,'nuc')
File "<__array_function__ internals>", line 5, in norm
File "D:\WinPython\WPy64-3820\python-3.8.2.amd64\lib\site-packages\numpy\linalg\linalg.py", line 2557, in norm
raise ValueError("Improper number of dimensions to norm.")
ValueError: Improper number of dimensions to norm.
``````

## Example Codes: `numpy.linalg.norm()` to Find the Vector Norm and Matrix Norm Using `axis` Parameter

We will find the vector norm first.

``````from numpy import linalg as la
import numpy as np

x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])

norm = la.norm(x,axis= 0)
print('The vector norm is:')
print(norm)
``````

Output:

``````The vector norm is:
[41.78516483 80.95060222 91.83136719]
``````

Note that the function has returned an N-dimensional `array` as the computed vector norm.

Now, we will compute the matrix norm. We will pass the `axis` parameter as the 2-`tuple` of integer value.

``````from numpy import linalg as la
import numpy as np

x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])

norm = la.norm(x,axis= (0,1))
print('The value of matrix norm is:')
print(norm)
``````

Output:

``````The value of matrix norm is:
129.35223229616102
``````

## Example Codes: `numpy.linalg.norm()` to Use `ord` Parameter

The parameter `ord` has several values.

``````from numpy import linalg as la
import numpy as np

x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])

norm = la.norm(x,'fro')
print('The value of matrix norm is:')
print(norm)
``````

Output:

``````The value of matrix norm is:
129.35223229616102
``````

The function has generated the value of `Frobenius` matrix norm.

``````from numpy import linalg as la
import numpy as np

x = np.array([[11, 12, 5], [15, 6,10], [10, 8, 12], [12,15,8], [34, 78, 90]])

norm = la.norm(x,'nuuc')
print('The value of matrix norm is:')
print(norm)
``````

Output:

``````The value of matrix norm is:
152.28781231351272
``````

The function has generated nuclear matrix norm. It is the sum of the singular values.

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