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It would be useful for the specification to state the expected result of an empty norm (related to the discussion in numpy/numpy#28343)
In #232, it was decided that sum and prod of empty arays should return 0 and 1 respectively, as these are the additive and multiplicative identites, and for min and max to leave the behavior explicitly undefined.
If we extend this logic to matrix_norm, it implies that for ord='fro' or ord='nuc', the result for an empty matrix should be 0.0, and for other values of ord the behavior is undefined.
Extending this logic to vector_norm, it implies that for an empty vector the p-norm should be 0.0 for positive p; the correct behavior for negative and infinite p are less clear to me.