文章目录
矩阵的秩,课本上是这么定义的:
- 先引入numpy模块
![python 线性代数:[9]求矩阵的秩](/2015/01/05/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B9%5D%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9/834344afa40f4bfba7e0dda3014f78f0f63618d1.jpg)
- 创建一个单位矩阵i
![python 线性代数:[9]求矩阵的秩](/2015/01/05/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B9%5D%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9/020e66f0f736afc31b3c7c92b119ebc4b64512d1.jpg)
- 计算单位矩阵i的秩
![python 线性代数:[9]求矩阵的秩](/2015/01/05/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B9%5D%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9/a84052086e061d95802574cf79f40ad163d9caa3.jpg)
- 改变一下i右下角元素的值,设置为0
![python 线性代数:[9]求矩阵的秩](/2015/01/05/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B9%5D%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9/1cd4147b02087bf4878f141ef0d3572c10dfcfa3.jpg)
- 重新计算矩阵的秩,得到3
![python 线性代数:[9]求矩阵的秩](/2015/01/05/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B9%5D%E6%B1%82%E7%9F%A9%E9%98%B5%E7%9A%84%E7%A7%A9/f392492c11dfa9ec194d15e060d0f703908fc1a3.jpg)
以下是我们用到的所有代码:
import numpy
i=numpy.eye(4)
i
array([[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]])
numpy.matrix_rank(i)
Traceback (most recent call last):
File “<pyshell#6>”, line 1, in
numpy.matrix_rank(i)
AttributeError: ‘module’ object has no attribute ‘matrix_rank’
numpy.linalg.matrix_rank(i)
4
i[-1,-1]=0
i
array([[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 0.]])
i[1,1]
1.0
numpy.linalg.matrix_rank(i)
3
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