Vector Definition Debate
Discussions center on the mathematical definition of vectors as elements of vector spaces versus geometric intuitions, including distinctions from matrices, tensors, and their use in linear algebra and machine learning contexts.
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Vectors are Nx1 matrices only once you choose an ordered basis!
Same with vectors!https://en.wikipedia.org/wiki/Vector_(mathematics_and_physic...
It's a vector in the mathematical sense.
I'm not sure I buy this after you just used an example of a 2d array of you're favorite colors just a few minutes ago. Maybe I'm missing something. What kind of linear transformation does that represent, and between what vector spaces?
you could also call it a matrix to modify a matrix in a vector space. not 100% correct. xD
Vector vs Matrices. Higher dimensional.
I'm actually not quite sure what you mean by breaking down into two-dimensional operations. We use operations on pairs of vectors, but nothing is assumed to be two-dimensional, and I don't think we suggest imagining anything as a plane? The vectors can be arbitrary and there's no assumption about curvature. Happy to clarify if I can help.
It's just an infinite-dimensional vector space ;-)
hmm ok but like… are u sure that’s not just fancy word math? like, when u “rotate” these vectors, how do u even know the meaning stays the same? wouldn’t it just… drift or get messy?idk maybe i’m dumb lol, just seems like it could get random real quick
this 3blue1brown video might answer your questionshttps://m.youtube.com/watch?v=8idr1WZ1A7Q