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Mar
11
comment Name of the generalization of quadtree and octree?
No, K-d tree obeys a different logic, and I am speaking of the generalization of quadtree/octree...
Mar
3
comment Is it true to say that every tensor is an element of a monoid?
Ok so, 1. what is a tensor, 2. what is the relation between monoids and tensor product ?
Mar
3
comment Is it true to say that every tensor is an element of a monoid?
So what is the most general algebraic structure on which the tensor product is defined ?
Mar
2
comment What is the most generic algebraic structure for which we can define a tensor product?
@ZevChonoles And in set theory (not category theory), what is the most generic mathematical object where we can form a product ?
Mar
2
comment What is the most generic algebraic structure for which we can define a tensor product?
@ZevChonoles I am not very fluent in category theory, but is it correct to say that we can always define a tensor product of two monoids?
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
Thanks. Last question if you have time: what are the extra properties I bring to point if I define them as members of a topological space (in the most general sense).
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
From the programming point of view, to declare an element (for runtime execution) one of the best option is to define the set it comes from at compile-time: when you declare a vector you can say "I take an element of this vector space". If you have the knowledge on affine space/topological space, could you elaborate on question 1./2. so I can upvote your explanation ?
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
See the edit...
Mar
1
comment Relations between an affine space and a topological space
See the edited question.
Feb
28
comment Origin in vector space?
Ok, so here origin means the null vector, not a "point" (my problem was that a point is not an element of a vector space, but an element of an affine space). Do you agree with that ?
Feb
27
comment Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system
I have good notions of set theory and linear algebra and I do not have big problem on these concepts taken separetely. But I do not have a clear picture of how to assemble and construct a coherent landscape with these concepts.
Dec
31
comment Square vs non-square tensors?
Are you sure of what you are saying because in some documents, authors seem to say that the second fundamental form is a tensor of type (2, 0) (see section 17.3 of this document: maths-people.anu.edu.au/~andrews/DG/DG_chap17.pdf, or page 171 of this document : win.tue.nl/~rvhassel/Onderwijs/Tensor-ConTeX-Bib/…)
Dec
31
comment Square vs non-square tensors?
Thank you very much. As I am not friendly at all with the second fundamental form, could you explain me what is exactly the number of dimension over each index?
Dec
31
comment Square vs non-square tensors?
Maybe the term non-square tensor was not well-chosen then. The Riemann curvature tensor in this denomination IS a square tensor (by square I mean non-hyperrectangle: same dimension over each index).
Dec
27
comment Irreducibility of gcd/lcm or lcm/gcd
@IgorRivin Yes, but I think that $r_3 \neq 1/r_4$
Dec
27
comment Irreducibility of gcd/lcm or lcm/gcd
@IanMateus: are you sure that they are symmetrical since in the first case, we take lcm of the two denominators, and in the second case, we take lcm of the two numerators?
Nov
11
comment Is the fraction of the irrational exponentiations of two coprime integers by a rational an irrational?
I edited the question (added "or an integer").
Nov
11
comment Can the exponentiation of an integer by a rational be a non-integer rational?
Thanks, I edited the question
Oct
23
comment What is the mathematical nature of a rotation matrix?
Thank you for your very detailed answer. So if I understand well, a rotation matrix can be viewed as a (1, 1) tensor from a mathematical point of view. Do you confirm that ?
Oct
6
comment Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?
I can remove the opinion-based part. But the question remains: "How numerical proofs are checked without access to the source code ?". For an open problem dated from 1742, just requiring the description of the algorithm does not seem to me as a deep verification. It's like describing a calculation procedure without requiring the actual calculation.