Thinking about this a bit more, this seems sensible, at least for square empty matrices. For square matrices, we define the condition number as $\Vert A \Vert \cdot \Vert A^{-1} \Vert$. For an empty matrix, the norm should be zero (because it's the additive identity), and the inverse of a square empty matrix is itself (since $Ax = b$ has a unique solution: an empty $b$ is unique, and empty $x$ solves it).

Returning 0 is also what Matlab does, it seems.

Agree, restricting to square A is reasonable.

Would be good to have a @test_throws to ensure it throws for non-square empty matrices.

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I am trying to understand the argumentation here. I see zero was the least breaking change. But in principle, for any consistent norm, we have
$$\kappa(A) = \lVert A\rVert \lVert A^{-1}\rVert \geq \lVert A A^{-1}\rVert = 1$$,
i.e. $$\kappa(A)$$ lies in the range $$[+1, +\infty]$$. Instead of saying that the empty matrix is the additive identity, one could also say that it is the multiplicative identity, which I think makes much more sense in the setting where one uses condition numbers. Indeed, as pointed out by @stevengj , $$A * x = b$$ where $$A$$ and $$b$$ are empty has a unique solution, namely also $$x$$ is empty or thus $$x = b$$ or thus $$A$$ is the (multiplicative) identity, and thus I would expect condition number $$\kappa(A)=1$$.

Never mind, reading the Matlab discussion linked to above made things a bit clearer. My apologies for the noise.