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That's fine, but then you shouldn't pretend that you're in a vector space. Words have meanings, and mathematical concepts have precise definitions.
by stephencanon 10y ago
That's fine, but then you shouldn't pretend that you're in a vector space. Words have meanings, and mathematical concepts have precise definitions.
- sp332 10y agoConstraining points to a hypersphere surface only reduces dimensionality by one dimension. For example a sphere in 3-space still has a 2-dimensional surface to play with. That's still a vector space right?
- stephencanon 10y agoNo; it's not closed under linear combinations and it doesn't contain an additive identity.
- sp332 10y agoWell it does if you use the right coordinate system! As the article mentions, most people don't normalize correctly and only get passable answers by luck. You can add locations on the earth's surface if you pick a point to be the origin.