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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.
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By definition, a matrix is singular and cannot be inverted if it has a determinant of zero. You can use the det() function from NumPy to calculate the determinant of a given matrix before you attempt to invert it: What is this? The determinant of our matrix is zero, which explains why we run into an error.
We use numpy. linalg. inv() function to calculate the inverse of a matrix. The inverse of a matrix is such that if it is multiplied by the original matrix, it results in identity matrix.
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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