机器学习笔记--1.2 Numpy的Linalg库

1.矩阵的行列式

from numpy import *
#n阶方阵的行列式运算
A = mat([[1, 2, 4, 5, 7], [9, 12, 11, 8, 2],[6, 4, 3, 2, 1], [9, 1, 3, 4, 5], [0, 2, 3, 4, 1]])
print("det(A):", linalg.det(A))

输出结果：

        det(A): -812.0

2.矩阵的逆

from numpy import *
A = c
invA = linalg.inv(A) #矩阵的逆
print("inv(A):", invA)

输出结果

        inv(A): [[-0.07142857 -0.01231527  0.05295567  0.09605911 -0.00862069]
         [ 0.21428571 -0.37684729  1.22044335 -0.46059113  0.3362069 ]
         [-0.21428571  0.82512315 -2.04802956  0.56403941 -0.92241379]
         [ 0.         -0.4137931   0.87931034 -0.17241379  0.81034483]
         [ 0.21428571 -0.06650246  0.18596059 -0.08128079 -0.14655172]]

3.矩阵的对称

from numpy import *
A = mat([[1, 2, 4, 5, 7], [9, 12, 11, 8, 2],[6, 4, 3, 2, 1], [9, 1, 3, 4, 5], [0, 2, 3, 4, 1]])
AT = A.T   #矩阵的对称
print(A * AT)

输出结果：

        [[ 95 131  43  78  43]
         [131 414 153 168  91]
         [ 43 153  66  80  26]
         [ 78 168  80 132  32]
         [ 43  91  26  32  30]]

4.矩阵的秩

from numpy import *
A = mat([[1, 2, 4, 5, 7], [9, 12, 11, 8, 2],[6, 4, 3, 2, 1], [9, 1, 3, 4, 5], [0, 2, 3, 4, 1]])
print(linalg.matrix_rank(A))

输出结果：

        5