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 libraryimport numpy as np# initialize vectorvec = np.arange(10)# compute norm of vectorvec_norm = np.linalg.norm(vec)print("Vector norm:")print(vec_norm) |
Output:
Vector norm: 16.881943016134134
The above code computes the vector norm of a vector of dimension (1, 10)
Example 2:
Python3
# import libraryimport numpy as np# initialize matrixmat = np.array([[ 1, 2, 3], [4, 5, 6]])# compute norm of matrixmat_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 libraryimport numpy as npmat = np.array([[ 1, 2, 3], [4, 5, 6]])# compute matrix num along axismat_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 libraryimport numpy as np# initialize vectorvec = np.arange(9)# convert vector into matrixmat = vec.reshape((3, 3))# compute norm of vectorvec_norm = np.linalg.norm(vec)print("Vector norm:")print(vec_norm)# computer norm of matrixmat_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.
