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> You might like to think of vectors in their geometric interpretation but vectors are not inherently geometric - vectors are just lists of numbers No. They ca
by bowsamic 2y ago
> You might like to think of vectors in their geometric interpretation but vectors are not inherently geometric - vectors are just lists of numbers
No. They can be expressed as lists of numbers in a basis if the vector space is equipped with a scalar product but the vector itself is an object that transcends the specific numbers it is expressed in.
What you’re saying here is totally wrong and I recommend you check out the Wikipedia page on vector spaces. The geometrical object “a vector” is the more fundamental thing than the list of numbers
- xigoi 2y agoTuples of numbers are a special case of a vector space, which even comes with a canonical basis and inner product for free. And since the article is about word embeddings, which map words to tuples of numbers, there’s no need to mention other vector spaces in this context.
- jameshart 2y agoYou think this comment could have been written by someone who doesn’t understand what a vector space is? Vectors are not purely geometric objects. Geometry is a lens through which we can interpret vectors. So is linear algebra. The objects behave the same and both perspectives give us insights about them. Insisting vectors are only geometric is like saying complex numbers are geometric because they can be thought of as points on the complex plane.