singular matrix python_如何确定一个矩阵在python-numpy中是否是奇异的？

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.

解决方案

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