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(Clarification of Iverson’s quote relating outer product to inner product. Copied from my personal “Talk” page since I accidentally started it there.) Tags: Mobile edit Mobile web edit |
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== Context for the Falkoff/Iverson quote == | |||
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 <syntaxhighlight lang=apl inline>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</syntaxhighlight> the enclosure of one axis of each argument, prior to the outer product operation, is responsible for the collapsing of dimensions. | 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 <syntaxhighlight lang=apl inline>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</syntaxhighlight> the enclosure of one axis of each argument, prior to the outer product operation, is responsible for the collapsing of dimensions. | ||