Linear Algebra usage numpy

Linear Algebra usage numpy

Matrix Multiplication

>>> import numpy as np
>>> x=np.array([[1,2,3],[4,5,6]])
>>> y=np.array([[7,8],[-1,7],[8,9]])
>>> x
array([[1, 2, 3],
       [4, 5, 6]])
>>> y
array([[ 7,  8],
       [-1,  7],
       [ 8,  9]])
>>> x.dot(y)
array([[ 29,  49],
       [ 71, 121]])
>>> np.dot(x,y)
array([[ 29,  49],
       [ 71, 121]])

Calculate the dot product

>>> a=np.array([[1,2],[3,4]])
>>> b=np.array([[11,12],[12,13]])
>>> np.vdot(a,b)
123

The formula is

result=1*11+2*12+3*12+4*13

Inner product

>>> np.inner(np.array([1,2,3]),np.array([0,1,0]))
2

The formula

result=1*0+2*1+3*0

Determinant calculation

>>> np.inner(np.array([1,2,3]),np.array([0,1,0]))
2
>>> a=np.array([[1,2],[3,4]])
>>> np.linalg.det(a)
-2.0000000000000004

Of Linear Equations

x + y + z = 6

2y + 5z = -4

2x + 5y - z = 27

Matrix representation

>>> import numpy as np
>>> a = np.array([[1,1,1],[0,2,5],[2,5,-1]])
>>> ainv = np.linalg.inv(a)#求矩阵的逆
>>> b = np.array([[6],[-4],[27]])
>>> x = np.linalg.solve(a,b)#求解需要A-1和B
>>> x
array([[ 5.],
       [ 3.],
       [-2.]])
>>>