Empty matrices are a perfectly normal mathematical object. Almost no one teaches them, but we should all have learned about them when we studied linear algebra, because they are necessary to make the whole theory work. Consider the function such that f(x) = 0 for each x\in \mathbb{R}^2. This is a perfectly fine linear map from \mathbb{R}^2 to the trivial vector space \{0\}, right? So there must be a matrix associated to it, and this matrix is necessarily zeros(0,2). [EDIT: fixed dimension order, as noted in the next message]
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