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

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

, norm

numpy.linalg

norm(x, ord=None, axis=None, keepdims=False)

DeterminantIn scipy.linalg, the determinant function is det

Apart from a

a. 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

trace

numpy

umpy.trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)

• 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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