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SO(3) dimensionality

  • RTR=I
  • detR=1

I.e.

⟨R[i,:],R[:,j]⟩=δij, i,j∈{1..3}2, total of
123⋅4=6 unique constraints for
9 variables

The

detR=1 constraint is redundant then

Last changed by 
 
Serge K
Yet another math guy.
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Riemannopt@HSE - SLIDES, pt. 1/2

Sketch of slides for the Riemann opts talk at HSE. View the slide with "Slide Mode".

Sep 17, 2023
Riemannopt@HSE - NOTES, pt. 1/2

https://hackmd.io/@newkozlukov/manopt-slides

Sep 17, 2023
torch.nn.functional.interpolate

Task: smoothing def smoothen_pillow(i: Image, f: int = 4): w, h = i.width, i.height assert w % f == 0 assert h % f == 0 i = i.resize((w // f, h // f), resample=BILINEAR) i = i.resize((w, h), resample=BILINEAR) return i PIL.Image.Image.resize(..., method=BILINEAR)

Nov 11, 2022
Untitled

Thanks! And now the links I've promised. First, I want to apologize for the manner of pitching things in the most objectionable form one can think of at a moment :upside_down_face: It's more fun this way though Second, I'd like to clarify, that I find that the subject actually is relevant: the word "tensor" is horribly overloaded and causes a lot of confusion even now. I'm not particularly familiar with the history of mathematics, but I suspect the word used to be used predominantly by physicists, and in the same sense as formalized later with differential geometry. Of course, the many loose possible meanings physicists may conjure up in their heads don't always coincide exactly with the formalization, and that's already one source of confusion. As the century of breaking the grounds of physics becomes more of a century of computation, it also makes more sense to talk just about "multidimensional arrays". Especially for computer scientists, or people dealing with discrete mathematics. Today we seem to have what one could call the "numerical (linear) algebra" community with their "tensor trains" and other "decompositions"[^tucker] who tend to purposefully forget where the structure of their "tensors" is coming from. I recall chatting to a student of a professor-not-unrelated-to-tensor-trains who, rather violently, denied that their "multidimensional arrays" have got anything to do with "tensors from physics, or with multilinear maps, or anything like it". It seems that to many physicists "tensors" really "are things that transform like tensors" (meaning they aren't anything concrete at all!), and they cannot quite make one step further. To these people I say: "why do you contract?".

Apr 26, 2022
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