User talk:⊂⍺m

The Falkoff/Iverson quote, while providing illuminating historical context, unfortunately is misleading—the reduction in inner product does not collapse any axes relative to the result shape, as it is applied only within each enclosure/box of the outer product. Rather, in ‪f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y‬ the enclosure of one axis of each argument, prior to the outer product operation, is responsible for the collapsing of dimensions.

Equivalently from a slightly different angle, if we use the model X⊂⍤(f/)⍤g⍤1⍤1 99⊢Y⍉⍨¯1⌽⍳≢⍴Y, the collapsing of dimensions is due more generally to ⊂⍤…⍤g⍤1 mapping two vectors to a scalar. Clearly the same holds for …⊂⍤g⍤1…, i.e., the same expression with the reduction removed.

I added a clarification about this in the article, but I’m wondering if there’s a better place to put said clarification. On one hand it seems a bit distracting in its current placement in the article. On the other hand, I feel it’s worth clarifying because this misconception has caused me confusion when experimenting with inner and outer products as an APL newcomer and trying to clarify their relation. The quote in question led me to incorrectly reason that the result should include all the axes of x and y if I remove the reduction from the IP model. More generally, it falsely implies that inner and outer product are much more simply related than they are in reality. (The confusion is not helped by the outdated syntax and/or general hairiness of the IP models given by ISO/IEC and Hui, respectively.)

Anyway, please do suggest any alternative placement/organization of the quote and its accompanying clarification that you feel will better serve the flow of the article.