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How to use Python to find the norm and determinant of a matrix
How to use Python to find the norm and determinant of a matrix
In the function of scipy.linalg, two parameters are often provided. One is check_finite. When it is True, a limited check will be performed. The other type is overwrite_xxxx, which indicates whether xxxx can be overwritten during the calculation process. For the sake of simplicity, it will be said later that a provides an overwrite switch, which means there is a parameter overwrite_a. When it is True, a is allowed to be overwritten during the calculation process; If a limited check switch is provided, it means that the check_finite parameter is provided.
Norm
The function norm is provided in scipy.linalg to find the norm, which is defined as
norm(a, ord=None, axis=None, keepdims=False, check_finite=True)
Whereord is used to declare the order of the norm
| Matrix norm | Vector norm | |
|---|---|---|
| Frobenius norm | 2-Norm | |
Frobenius norm | - | |
Nuclear norm | -##inf | |
| max ( ∣ a ∣ ) | | -inf|
| min ( ∣ a ∣ ) | | 0- |
1 | max(sum(abs(a), axis=0))||
| -1||
| 22-Norm (maximum singular value) | |
| -2 | Minimum singular value | |
| ## If | a is a vector, if | ord
nuclear norm The number is also called the "trace norm" and represents the sum of all singular values of the matrix. Frobenius norm can be defined as

The essence is the natural generalization of the 2-norm of vectors in matrices.
In addition to
scipy.linalg,
norm
numpy.linalg
, and its parameters arenorm(x, ord=None, axis=None, keepdims=False)
The optional parameters of order are the same as the norm function in scipy.linalg. DeterminantIn scipy.linalg, the determinant function is det
Apart from a
, there are only override switches and limited checks ofa. The example is as follows
import numpy as np from scipy import linalg a = np.array([[1,2,3], [4,5,6], [7,8,9]]) linalg.det(a) # 0.0 a = np.array([[0,2,3], [4,5,6], [7,8,9]]) linalg.det(a) # 3.0
tracescipy.linalg does not provide the trace
function, butnumpy
Provided, it is defined asumpy.trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)
whereoffset is the offset, indicating the offset relative to the main diagonal
axis1, axis2
represents the coordinate axis- ##dtype
The data type used to adjust the output value
>>> x = np.random.rand(3,3) >>> print(x) [[0.26832187 0.64615363 0.09006217] [0.63106319 0.65573765 0.35842304] [0.66629322 0.16999836 0.92357658]] >>> np.trace(x) 1.8476361016546932
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