The norm of a size zero array should be zero.

Just as the empty sum is 0 and the empty product is 1, the empty norm should be 0 in my opinion. In numpy, this convention has been implemented and is unit-tested for the default vector and matrix norms:

    def test_empty(self):
        assert_equal(norm([]), 0.0)
        assert_equal(norm(array([], dtype=self.dt)), 0.0)
        assert_equal(norm(atleast_2d(array([], dtype=self.dt))), 0.0)

Some of the non-default empty norms raise exceptions. The induced matrix 2-norm raises exceptions for two reasons – first, attempting to compute the singular values of a size-0 matrix raises an exception, and second, even if the the empty array of singular values were to be returned, attempting to compute the max of an empty sequence also raises an exception. The empty induced matrix 1-norm and np.inf-norm each also raise an exception because they try to compute an empty max.

[ewmoore]

On Monday, January 5, 2015, argriffing [e-mail] wrote:

Personally I’d like to have max_abs and sum_abs numpy ufuncs. Unlike max, the max_abs ufunc could have empty max 0. Also these ufuncs could save time and memory, but of course they would bloat the code, pollute the namespace, and invite discussion about which other combinations should be added. Yesterday I looked at adding these myself, but I was too intimidated by the code.

— Reply to this email directly or view it on GitHub https://github.com/numpy/numpy/issues/5420#issuecomment-68746069.

Since the first and obvious use would be in linalg.norm perhaps they could be added, and exposed only through there. If doing so, it might be worth copying the dnrm2 algorthm too instead of calling dot as norm does now.

[seberg]

Closing as duplicate as noted by Eric. (inf norm on empty array raising error since it calls max([])). It sounds like there may have been more issues here, but those have been resolved.