User talk:⊂⍺m

The Falkoff/Iverson quote, while providing illuminating historical context, is a bit 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.

⊂⍺m (talk) 22:45, 25 June 2023 (UTC) ⊂⍺m