How to use Python to find the norm and determinant of a matrix

In the function ofscipy.linalg, two parameters are often provided. One ischeck_finite. When it isTrue, a limited check will be performed. The other type isoverwrite_xxxx, which indicates whetherxxxxcan be overwritten during the calculation process. For the sake of simplicity, it will be said later thataprovides an overwrite switch, which means there is a parameteroverwrite_a. When it isTrue, a is allowed to be overwritten during the calculation process; If a limited check switch is provided, it means that thecheck_finiteparameter is provided.

Norm

The functionnormis provided inscipy.linalgto find the norm, which is defined as

norm(a, ord=None, axis=None, keepdims=False, check_finite=True)

Whereordis used to declare the order of the norm

##ord Matrix norm Vector norm #None 'fro' ##'nuc' - ##max(sum(abs(a), axis=1)) max ⁡ ( ∣ a ∣ ) -inf min(sum(abs(a), axis=1)) min ⁡ ( ∣ a ∣ ) 0 - ##sum(a!= 0) max(sum(abs(a), axis=0)) -1 min(sum(abs(a), axis=0)) 2 -2 ## If ord is a non-zero integer, recorded as n nn. Let a i a_iai be the elements in matrix a aa, then the n nn norm of the matrix is

Frobenius norm	2-Norm
Frobenius norm	-
Nuclear norm		##inf
		1
		2-Norm (maximum singular value)
		Minimum singular value
		a is a vector, if

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

is also provided in

numpy.linalg

, and its parameters are

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

The optional parameters oforder are the same as thenorm function inscipy.linalg

.

DeterminantInscipy.linalg, the determinant function isdet

, and its definition is very simple, except for the matrix to be found

Apart from a

, there are only override switches and limited checks of

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 scipy.linalg

does not provide the

trace

function, but

numpy

Provided, it is defined as

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

where offset

is the offset, indicating the offset relative to the main diagonal

• axis1, axis2represents 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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