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129 lines
1.4 KiB
Markdown
129 lines
1.4 KiB
Markdown
# 矩阵
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使用 `mat` 方法将 `2` 维数组转化为矩阵：
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In [1]:
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```py
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import numpy as np
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a = np.array([[1,2,4],
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[2,5,3],
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[7,8,9]])
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A = np.mat(a)
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A
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```
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Out[1]:
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```py
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matrix([[1, 2, 4],
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[2, 5, 3],
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[7, 8, 9]])
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```
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也可以使用 **Matlab** 的语法传入一个字符串来生成矩阵：
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In [2]:
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```py
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A = np.mat('1,2,4;2,5,3;7,8,9')
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A
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```
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Out[2]:
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```py
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matrix([[1, 2, 4],
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[2, 5, 3],
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[7, 8, 9]])
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```
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利用分块创造新的矩阵：
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In [3]:
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```py
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a = np.array([[ 1, 2],
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[ 3, 4]])
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b = np.array([[10,20],
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[30,40]])
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np.bmat('a,b;b,a')
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```
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Out[3]:
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```py
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matrix([[ 1, 2, 10, 20],
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[ 3, 4, 30, 40],
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[10, 20, 1, 2],
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[30, 40, 3, 4]])
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```
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矩阵与向量的乘法：
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In [4]:
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```py
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x = np.array([[1], [2], [3]])
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x
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```
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Out[4]:
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```py
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array([[1],
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[2],
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[3]])
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```
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In [5]:
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```py
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A * x
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```
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Out[5]:
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```py
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matrix([[17],
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[21],
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[50]])
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```
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`A.I` 表示 `A` 矩阵的逆矩阵：
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In [6]:
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```py
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print A * A.I
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```
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```py
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[[ 1.00000000e+00 0.00000000e+00 0.00000000e+00]
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[ 0.00000000e+00 1.00000000e+00 2.08166817e-17]
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[ 2.22044605e-16 -8.32667268e-17 1.00000000e+00]]
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```
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矩阵指数表示矩阵连乘：
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In [7]:
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```py
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print A ** 4
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```
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```py
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[[ 6497 9580 9836]
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[ 7138 10561 10818]
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[18434 27220 27945]]
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``` |