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I think that calling it outer product makes more sense https://arxiv.org/pdf/1905.01289v1.pdf https://arxiv.org/pdf/1905.01289v1.pdf.
by adamnemecek 6y ago
I think that calling it outer product makes more sense https://arxiv.org/pdf/1905.01289v1.pdf https://arxiv.org/pdf/1905.01289v1.pdf.
- Tomminn 6y agoThe type signature of the outer product is not correct. We are mapping two functions to a function in the same domain. Convolution is neither a valid example of an inner product or an outer product. No basic geometric operation on vectors has the correct type signature and axioms for convolution to be interpreted as a generalized "x". What we'd be looking for is a billinear mapping of vectors to vectors, and complex number style multiplication in R^2, or cross product multiplication in R^3 or R^7 are the only real candidates in that category unless we start interpreting functions as matrices.
- adamnemecek 6y agoOk, exterior product.
- Tomminn 6y agoThe exterior product also exists in a different vector space to its factors.