如何确定一个矩阵在python-numpy中是否是奇异的?

问题描述

我不确定python-numpy是否可以帮助我们确定矩阵是否为奇数.我试图根据行列式进行决定，但是numpy会在1.e-10左右产生一些值，并且不确定应该为临界值选择什么.

I am not sure whether python-numpy can help us decide whether a matrix is singular or not. I am trying to decide based on the determinant, but numpy is producing some values around 1.e-10 and not sure what should we choose for a critical value.

推荐答案

在默认公差下使用np.linalg.matrix_rank.关于该函数的文档字符串有一些讨论，关于考虑零的奇异值的适当截止点是什么:

Use np.linalg.matrix_rank with the default tolerance. There's some discussion on the docstring of that function on what is an appropriate cutoff to consider a singular value zero:

>>> a = np.random.rand(10, 10)
>>> b = np.random.rand(10, 10)
>>> b[-1] = b[0] + b[1] # one row is a linear combination of two others
>>> np.linalg.matrix_rank(a)
10
>>> np.linalg.matrix_rank(b)
9
>>> def is_invertible(a):
...     return a.shape[0] == a.shape[1] and np.linalg.matrix_rank(a) == a.shape[0]
...
>>> is_invertible(a)
True
>>> is_invertible(b)
False

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