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# /sci/ - Science & Math

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What is tensor?
Define tensor in C#.
Is it some kind of array?

 >> Anonymous Wed Jun 24 07:07:59 2020 No.11831692 >>11831690>Is it some kind of array?Yes. Essentially an n-d array.
 >> Anonymous Wed Jun 24 07:13:59 2020 No.11831702 >>11831690matrix is a nice gimmick for rank-2 tensors, but it is just a comfy blanket, it all falls apart when the rank goes higher than 2.this guy's style is silly, but bear with it, it gives a good general picture of tensors for beginnershttps://youtu.be/bpG3gqDM80w
 >> Anonymous Wed Jun 24 07:22:44 2020 No.11831718 Tensor is as much of an array as a triangle is an array of numbers. You can even consider proofs to be arrays of numbers. The fact that someone can be reduced to an array of numbers in some particular situation with some particular choices, doesn't mean it's "essentially just an array of numbers". Only low -IQ mathlet with no conception of higher order concepts can think that way.
 >> Anonymous Wed Jun 24 07:50:09 2020 No.11831757 File: 237 KB, 1000x2349, computer science.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Jun 24 07:53:12 2020 No.11831764 >>11831718>Only low -IQ mathlet with no conception of higher orderIt's quite contrary. People with higher iq are better at generalizing aren't they? You can't call someone low-iq for him making higher generalzation. In short, you are contradicting yourself.
 >> Anonymous Wed Jun 24 08:06:39 2020 No.11831794 >>11831757Based. Fuck autistic CSfags who are too stupid to properly understand anything.An $(r,s)$ tensor is a multilinear map $(V^*)^r\times V^s \to \mathbb{F}$ where $V$ is a vector space over $\mathbb{F},$ and $V^*$ is the dual of $V.$
 >> Anonymous Wed Jun 24 08:09:08 2020 No.11831799 >>11831690tensor is a certain abstract quantity which can be represented by an array of numbers, in general more than 2-dimensional, once coordinates have been chosen. if we change the coordinates, the numbers also change, and they do so according to a certain transformation law. physicists and engineers usually take this transformation law as the definition of tensors which leads to the phrase "tensor is something which transforms as a tensor".
 >> Anonymous Wed Jun 24 08:13:18 2020 No.11831806
 >> Anonymous Wed Jun 24 08:15:31 2020 No.11831811 >>11831757BASED BACHELOR DEGREEand he's right, you know
 >> Anonymous Wed Jun 24 09:46:08 2020 No.11832043 >>11831690A tensor is an element of a tensor product, being a space of multilinear functions./thread
 >> Anonymous Wed Jun 24 09:53:41 2020 No.11832060 >>11832043>Writing an incorrect definition, then threading yourself, even though a better, correct definition is already written.Retard.
 >> Anonymous Wed Jun 24 10:00:27 2020 No.11832083 >>11831690OP is a CS faggot.
 >> Anonymous Wed Jun 24 10:10:18 2020 No.11832115 >>11832060>>>11832043 (You) #>>Writing an incorrect definition, then threading yourself, even though a better, correct definition is already written.>Retard.Brainlet. My definition is more correct.
 >> Anonymous Wed Jun 24 10:19:02 2020 No.11832144 >>11832115>An element of a tensor productA tensor product is not a set, and you haven't defined a tensor product.>being a space of multilinear functionsYou don't specify what you are referring to here.Also, you don't make reference to rank.Your definition is suggestive of a high schooler who read an article about tensors a month ago and now thinks he's the authority on them.
 >> Anonymous Wed Jun 24 10:25:19 2020 No.11832159 >>11832144stop this madness. the anon's explanation is awful, but nothing he wrote is incorrect.
 >> Anonymous Wed Jun 24 10:30:02 2020 No.11832172 >>11832159Fine, I'll change my contention to that.
 >> El Arcón Wed Jun 24 10:30:25 2020 No.11832175 File: 1.20 MB, 400x267, TIMESAND___4cookie-monster-100-years-of-cookie-history-video-0.gif [View same] [iqdb] [saucenao] [google] [report] >>11831690In general, a tensor is map from vectors to vectors. Depending on the number of indices, it might be a map from vectors to numbers or from vectors to another tensor.Tensors eat vectors.
 >> El Arcón Wed Jun 24 10:32:45 2020 No.11832182 Also, if you want a deeper understanding of tensors, then look at the 3D stress tensor. It has a nice wiki that explains how each component of the tensor is the pressure or shear force on each face of a cube pushing in each direction. Then you can contract it with a vector and see what happens, and then it's pretty easy to understand what it means when I say "tensors eat vectors."
 >> Anonymous Wed Jun 24 10:40:12 2020 No.11832200 a (p,q) tensor can be thought as some abstract thing eats q vectors and returns p of them, or eats p+q and gives you a number, or any arbitrary combination of which arguments to eat or spit out vectors such that its always linear in each of the p+q argumentsthe rigorous concepts of multilinearity, dual space and isomorphisms are what let you do this and let you represent them as a p+q dimensional array of numbers
 >> Anonymous Wed Jun 24 10:43:35 2020 No.11832205 >>11832200I should also say that "returning 0 vectors" means returns a number/scalari.e. a billinear form/metric is (0,2) because it eats 2 vectors and returns their inner product which is a number = 0 vectors returned, but with extra structure you can shuffle things around to a (1,1) endomorphism/linear map which you supply 1 vector and are given 1 vector, both are represented by 1+1=2+0 dimensional arrays.
 >> Anonymous Wed Jun 24 11:02:35 2020 No.11832236 >>11831690>is it some kind of array It would be recursively defined using arrays, but they are not themselves exactly arrays or matrices. They are a certain generalization of vector spaces whose construction will become obvious with study into linear algebra despite remaining annoying to work with >>11831757>tee here implementation is the same as the definition I bet you think CS majors would say the approximation for inverse square root is the definition of an inverse square root.
 >> Anonymous Wed Jun 24 11:20:31 2020 No.11832276 >>11832236>>tee here implementation is the same as the definition>I bet you think CS majors would say the approximation for inverse square root is the definition of an inverse square root.Dude just look at>>11831692clearly a lot of people think that tensors are just multidimensional arrays of numbers
 >> Anonymous Wed Jun 24 11:31:55 2020 No.11832308 Why do you even have to ask?It's obvious just from your picture that a tensor is an item with N dimensions where each dimension can contain a defined amount of values
 >> Anonymous Wed Jun 24 11:33:55 2020 No.11832313 >>11832308That's totally wrong and retarded.
 >> Anonymous Wed Jun 24 11:35:51 2020 No.11832318 >C#You have bigger problems in your life to solve buddy
 >> Anonymous Wed Jun 24 11:36:23 2020 No.11832320 >>11832308nope
 >> Anonymous Wed Jun 24 11:37:00 2020 No.11832322 >>11831794I'm retarded but curious, do you mind elaborating?
 >> Anonymous Wed Jun 24 11:56:49 2020 No.11832366
 >> Anonymous Wed Jun 24 12:10:51 2020 No.11832398 >>11832322I'll assume you already know what a vector space is.If $V$ is a vector space over a field $\mathbb{F},$ then its dual space $V^*$ is the space of linear maps (called functionals) that take elements of $V$ to elements of $\mathbb{F}.$ A concrete example would be to think of elements of $V$ as being column vectors, and then elements of $V^*$ are row vectors - check that under usual matrix multiplication, a row vector premultiplying a column vector results in a scalar.Now a map $\phi:V_1\times V_2\times ... \times V_n\to\mathbb{F}$ is multilinear if it is linear in every variable - e.g. recall that $\phi(v_1,v_2)$ is linear in its first entry if $\phi(av_1+w,v_2)=a\phi(v_1,v_2)+\phi(w,v_2),$ where $a\in\mathbb{F},$ and $w,v_1,v_2\in V.$So now suppose you have some $(r,s)$ tuple, $(w_1^*,w_2^*,...,w_r^*,w_1,w_2,...,w_s),$ where the $w_i^* \in V^*,$ and the $w_j\in V$ (note that e.g. $w_1$ isn't necessarily related to $w_1^*$ ). Then an $(r,s)$ tensor would act on that tuple and return a scalar, i.e. an element of the field $\mathbb{F}.$
 >> Anonymous Wed Jun 24 12:35:36 2020 No.11832455 >>11832322>>11832398Now given some vectors $v_1,...,v_r\in V$ and $v_1^*,...,v_s^*\in V^*,$ we can define an $(r,s)$ tensor as $v_1\otimes...\otimes v_r\otimes v_1^*\otimes ...\otimes v_s^*,$ which acts on an $(r,s)$ tuple (in post above) as [eqn] v_1\otimes...\otimes v_r\otimes v_1^*\otimes ...\otimes v_s^*(w_1^*,...,w_r^*,w_1,...,w_s)=w_1^*(v_1)...w_r^*(v_r)v_1^*(w_1)...v^*(s)(w_s), [/eqn] recalling that functionals act on vectors to give a scalar. Now an $(r,s)$ tensor needn't act only on an $(r,s)$ tuple. It can act on any tensor - for example [eqn] v_1\otimes...\otimes v_r\otimes v_1^*\otimes ...\otimes v_s^*(w_1,...,w_s)=v_1^*(w_1)...v_s^*(w_s)v_1\otimes ...\otimes v_r. [/eqn] There we see an $(r,s)$ tensor acting on a $(0,s)$ tuple (or a $(s,0)$ tensor - see below) to give us a $(r,0)$ tensor. Hopefully you can see what rank you get when it acts on an arbitrary tensor.Now just note that the set of tuples $(w_1^*,...,w_r^*,w_1,...,w_s)$ has a one to one correspondence with the set of $(s,r)$ tensors, $w_1\otimes ...\otimes w_s\otimes w_1^*\otimes ...\otimes w_r^*,$ which shows why it is natural to allow tensors to act on arbitrary tensors.
 >> Anonymous Wed Jun 24 12:40:24 2020 No.11832469 >>11831692fpbp>>11832398>>11832276>>11832236>>11832313>>11832320>>11832175>>11832043>>11832060>>11832115>>11831757>>11831794>>11831718>>11831702>define tensor in C#>in C#>b-but it's not an array!Wanna know why I know for a fact you're the same fags who refuse to use serious programming languages even if it will get your work done faster?
 >> Anonymous Wed Jun 24 12:41:01 2020 No.11832470 >>11832398>>11832455Is this what mathfags find interesting?This is just pure autism
 >> Anonymous Wed Jun 24 12:52:08 2020 No.11832511 >>11832470>Is this what mathfags find interesting?No>This is just pure autismYeah, no shit; it's basically a single definition padded with elaboration as anon asked for.The definition right here >>11831794 demonstrates about the amount of thought that a mathfag would put into it.
 >> Anonymous Wed Jun 24 12:57:41 2020 No.11832531 >>11832469how to BTFO /sci/
 >> Anonymous Wed Jun 24 14:05:49 2020 No.11832773 >>11832398>>11832455I've done a lot of linear algebra between QM, but the notation is just so dense for me you know? I'll try to digest this.
 >> Anonymous Wed Jun 24 14:20:32 2020 No.11832836 >>11831690gradient of a field is a vector field. gradient of a vector field is a tensor. subsequent gradients of those vector fields are tensors of increasing order.
 >> Anonymous Wed Jun 24 14:29:21 2020 No.11832873 >>11832175Thanks, my understanding isn't beyond an array of numbers, but this definition helps me most
 >> Anonymous Wed Jun 24 15:23:38 2020 No.11833087 >>11832469>multiple answers saying “it’s not an array but any implementation would use them in the definition”>hurr you guys don’t know prongramminYou’re illiterate, stupid, or both.
 >> Anonymous Wed Jun 24 17:07:54 2020 No.11833477 >>11832276>clearly a lot of people think that tensors are just multidimensional arrays of numbersI do not think that they are *just* that, but if you want to break it down to the simplest description "an n-d array" is exactly what you want.
 >> Anonymous Wed Jun 24 17:30:55 2020 No.11833564 >>11832398You fucking incel
 >> Anonymous Wed Jun 24 17:42:33 2020 No.11833596 >>11832455why does advanced maths have so many white power symbols
 >> Anonymous Wed Jun 24 20:06:25 2020 No.11834002 >>11831690It's a list of numbers used in a data science model. Say you have some sensors for picking up weather data and you want to find out if it's going to rain. The numbers inputted into the function from those sensors, the lists of other numbers they are used in operations with (like matrix multiplication for example), and the single number the function outputs (a list can be just 1) are all tensors.
 >> Anonymous Wed Jun 24 20:11:12 2020 No.11834012 >>11831794/threadSome intuition: Break down into covariant and contravariant cases.1d) A map V->F is basically an element of V*1d) A map V*->F is basically a vector2d) A map VxV->F is a bilinear map, can be thought of as an abstraction of area in some senseFor other cases, there's lots of ways to think about it by "(un)currying". For example, a map VxV*-->F can be thought of as V-->Hom(V*,F)=V**=V, so is basically an endomorphism. They're literally just covariant and contravariant multilinear maps involving a single vector space, its dual, and underlying field.
 >> Anonymous Thu Jun 25 01:41:47 2020 No.11834680 >>11834002>It's a list of numbers used in a data science model.Lol. Are you retarded?> The numbers inputted into the function from those sensorsWhich weather sensor has a digital data input? WTF are you on about?> the listsLol.A list is not a tensor you fucking idiot. They are not even arrays.
 >> Anonymous Thu Jun 25 01:50:44 2020 No.11834686 >>11831690A tensor is an object that transforms like a tensor.t. physichad
 >> Anonymous Thu Jun 25 02:48:08 2020 No.11834763 >>11834002Wtf
 >> Anonymous Thu Jun 25 03:13:51 2020 No.11834810 >>11831690It's a generalization of matrices.
 >> Anonymous Thu Jun 25 04:29:49 2020 No.11834965 Can every tensor be expressed as an n-dimensional array? Yes or no? I don't care about whether that's the actual definition. I just want to know if it's equivalent.
 >> Anonymous Thu Jun 25 04:39:42 2020 No.11834984 >>11831794So how do you do this in code?
 >> Anonymous Thu Jun 25 05:03:00 2020 No.11835007 >>11834984A tensor can be described through its actions upon the basis vectors, so you can just write down the definition. For the finite dimensional case the dual is just the Vector space of linear maps from a given vector space to the reals. So you have a mapping which goes from a tuple of elements of the duals and a tuple of elements of the vector space to some arithmetic type, this is really simple stuff.
 >> Anonymous Thu Jun 25 05:06:02 2020 No.11835013 >>11831690>C#.>>>/g/et out and stay out
 >> Anonymous Thu Jun 25 05:06:15 2020 No.11835014 >>11831718what is a tensor but not an array? let’s start with rank 2 / matrix to keep it simple
 >> Anonymous Thu Jun 25 05:08:22 2020 No.11835017 >>11831794>understanding>while it’s purely knowledge based
 >> Anonymous Thu Jun 25 05:14:10 2020 No.11835027 >>11834984I'd assume it's pretty straightforward. I don't know much about coding, and I only really know C, but I think you can create a struct, with two sets of arrays - one for the covariant, one for the contravariant indices. It's obvious how you can then define multiplication, etc.Coding with tensors is not really interesting at all; it's just menial busy-work.
 >> Anonymous Thu Jun 25 05:28:36 2020 No.11835040 >>11835014the linear map $\frac{d}{dx} \colon C^{\infty}(\mathbb{R}) \to C^{\infty}(\mathbb{R})$
 >> Anonymous Thu Jun 25 05:34:20 2020 No.11835047 >>11835040what is this?and why does it not look like anon’s definition of V* x V -> F
 >> Anonymous Thu Jun 25 05:37:43 2020 No.11835051 >>11835047tensor-hom adjunction. any map $V^* \times V \to \mathbb{F}$ is the same as (naturally corresponds to) a map $V \to V$.
 >> Anonymous Thu Jun 25 05:40:23 2020 No.11835054 >>11835051that is neat. But wouldn’t this lose some form of information from F?And your example is basically an array that contains operators instead of numbers right?
 >> Anonymous Thu Jun 25 05:43:21 2020 No.11835056 >>11835054>But wouldn’t this lose some form of information from F?no, the underlying field is an information which comes with the vector space V>And your example is basically an array that contains operators instead of numbers right?no. tensors are not "basically an array" and this is no exception. this anon (I'm not him) >>11831718 is right and his analogy with the triangle is spot on.
 >> Anonymous Thu Jun 25 05:47:21 2020 No.11835064 >>11835056not that guy, but how is the triangle example spot on? *every* triangle can be reduced to a set of numbers, not just some particular cases. whether this is a useful interpretation is not directly important
 >> Anonymous Thu Jun 25 05:49:03 2020 No.11835066 >>11835056well if I understand your example correctly, the only thing that prevents me from writing it as an array is that it contains infinite elements. which really is “basically an array”
 >> Anonymous Thu Jun 25 05:55:20 2020 No.11835072 >>11835066btfo
 >> Anonymous Thu Jun 25 06:02:32 2020 No.11835082 >>11835064>*every* triangle can be reduced to a set of numbers, not just some particular cases.in the exact same way as *every* tensor can be reduced to a set of numbers>>11835066is it so incomprehensible that just because you can represent something as an array doesn't mean it's "basically an array" ?
 >> Anonymous Thu Jun 25 06:13:20 2020 No.11835096 >>11835064>>11835066>>11835014Let me write down (2,3,6,1,4123,512313,621323,3213123,6422,12323,232). Tell me what mathematical object this represents.
 >> Anonymous Thu Jun 25 06:17:50 2020 No.11835104 >>11835096>Tell me what mathematical object this represents.A tuple, up to embedding.
 >> Anonymous Thu Jun 25 06:18:37 2020 No.11835106 >>11835096Let me tell you what it represents: it's 2 vectors in R^5. Did you get it right?
 >> Anonymous Thu Jun 25 06:19:46 2020 No.11835107 File: 889 KB, 240x160, 1582738939565.gif [View same] [iqdb] [saucenao] [google] [report] >>11835104Wrong! You must be an idiot!>>11835106Here I actually lied! It's not 2 vectors in R^5, it's actually the polynomial 2 + 3x + 6x^2 + 4123x^3 +... ! I bet you feel stupid now, don't you?
 >> Anonymous Thu Jun 25 06:21:28 2020 No.11835109 >>11835082>*every* tensor can be reduced to a set of numbersWhich set of numbers is >>11835040?>>11835066If you were to write down that set is 5 in it?
 >> Anonymous Thu Jun 25 06:23:09 2020 No.11835110 >>11835107>it's actually the polynomial 2 + 3x + 6x^2 + 4123x^3 +... !The tuples can be embedded into the polynomials, so clearly I was right.By the way, this is how polynomials are usually implemented in software, as tuples.
 >> Anonymous Thu Jun 25 06:23:42 2020 No.11835111 File: 3.31 MB, 348x420, funnymonkeyreadsbook.gif [View same] [iqdb] [saucenao] [google] [report] >>11835107I actually lied here as well! It's neither a polynomial nor a pair of vectors in R^5. It's actually a 2-simplex (a triangle) embedded in R^3 that is the convex hull of the points with coordinates (6,1,4123), (512313,621323,3213123), (6422,12323,232)! How crazy is that! You must be a retard if you couldn't immediately spot that this is a triangle.
 >> Anonymous Thu Jun 25 06:27:50 2020 No.11835115 File: 3.12 MB, 400x296, 1576493903995.gif [View same] [iqdb] [saucenao] [google] [report] >>11835110Literally everything in maths can be represented as an array of numbers you fucking autistic retard, that's my whole fucking point. The fact that something can be embedded as an array of numbers doesn't mean that it's essentially an array of numbers. You lose almost all information the moment you encode it as an array of numbers all of which you need to keep in your head to be able to understand what is going on. If that were not the case you would be immediately able to say what mathematical object I mean by(2,3,1,2,3,4,122,5124,2323)Holy fucking shit the absolute state of this board.
 >> Anonymous Thu Jun 25 06:27:56 2020 No.11835116 >>11835111Still a tuple up to embedding.
 >> Anonymous Thu Jun 25 06:28:24 2020 No.11835118 File: 13 KB, 366x54, 2020-06-25 03-27-34.jpg [View same] [iqdb] [saucenao] [google] [report] >>11833087>Not an arrayHold on let me just
 >> Anonymous Thu Jun 25 06:29:13 2020 No.11835121 >>11835109pick some basis $\alpha = (f_i)$ of $C^{\infty}(\mathbb{R})$, put $a^i_j = i$-th coordinate of $\frac{d}{dx}f_j$ with respect to $\alpha$. $(a^i_j)$ is the array.
 >> Anonymous Thu Jun 25 06:30:14 2020 No.11835122 >>11835115>Literally everything in maths can be represented as an array of numbersSee >>11835109.
 >> Anonymous Thu Jun 25 06:31:22 2020 No.11835124 >>11835122>See >>11835109.see >>11835121
 >> Anonymous Thu Jun 25 06:32:36 2020 No.11835127
 >> Anonymous Thu Jun 25 06:33:08 2020 No.11835129 >>11835121But you can not reconstruct the tensor from the array alone. Clearly they can not be identified.Try again.
 >> Anonymous Thu Jun 25 06:34:10 2020 No.11835131 >>11835124>>>11835122 (You) #>>See >>11835109 (You) #.>see >>11835121 #See >>11835129
 >> Anonymous Thu Jun 25 06:34:58 2020 No.11835132
 >> Anonymous Thu Jun 25 06:36:52 2020 No.11835134 >>11835096depends on what the brackets entail, for me it’s a standard vector.
 >> Anonymous Thu Jun 25 06:37:40 2020 No.11835135 >>11835134For me, it's a N=11, tuple.
 >> Anonymous Thu Jun 25 06:37:43 2020 No.11835136 File: 69 KB, 692x1024, 409.jpg [View same] [iqdb] [saucenao] [google] [report] >>11835122You're missing the fucking point. Whenever you have a well-defined mathematical object you can encode the definition to numbers. I can encode the definition "let x be the smallest natural number such that x has more than 300 distinct divisors". I can translate every character into a number and that way faithfully represent this number as an array of numbers, each of whose entry represents a character of my definition.The point that I'm making is that while this is used to implement computations with a lot of mathematical objects, the fact that you can do it in no way implies that the mathematical object itself is merely the numerical representation that your implementation uses. Implicit in this implementation is the very numerous assumptions that you hold in your head of what the numers in your implementations actually represent. The numbers just by themselves are meaningless. As I've demonstrated in the previous example >>11835096>>11835106>>11835107>>11835111, you can write down an array of numbers that can represent a vast multitude of completely different mathematical objects. Just by looking at the array of numbers it is IMPOSSIBLE to tell what mathematical object it is. This means that mathematical objects such as vectors, triangles, tensors are NOT just arrays of numbers. They can be represented and implemented BY arrays of numbers just like literally everything else in maths but that IN NO WAY implies that arrays of numbers is all that they are. The most important part of the object is not the array of numbers but the implicit meaning you hold in your head of what those numbers represent.
 >> Anonymous Thu Jun 25 06:38:23 2020 No.11835137 >>11835129I don't see what's your point now. if you got confused, my point is that every tensor can be represented by an array, but it's not an array per se.
 >> Anonymous Thu Jun 25 06:40:35 2020 No.11835138 >>11835135what’s the difference?
 >> Anonymous Thu Jun 25 06:41:20 2020 No.11835139 >>11835138The implementation.
 >> Anonymous Thu Jun 25 06:41:58 2020 No.11835140 >>11835115so every tensor is an array but not every array is a tensor?
 >> Anonymous Thu Jun 25 06:42:41 2020 No.11835142 >>11835137>I don't see what's your point now.What you wrote down is a tuple, up to embedding.Which means it does not carry the "meta" information about it.>>11835136and?
 >> Anonymous Thu Jun 25 06:44:46 2020 No.11835145 >>11835140>so every tensor is an arrayA tensor is not an array. A given tensor can be REPRESENTED by an array in infinitely many ways, just like literally every other well-defined mathematical object. But the moment you represent it as an array, a stranger looking at the array would have no idea what it is unless you tell him that it's actually a REPRESENTATION of a tensor.
 >> Anonymous Thu Jun 25 06:45:17 2020 No.11835146 File: 166 KB, 945x261, 1518301580940.png [View same] [iqdb] [saucenao] [google] [report] >>11832398>>11832455this is why I hate math. All the definitions are fucking autistic shit just throwing symbols and big words around which give you no idea of how it works. Then you do one example and find out you just do some stupid simple shit and it all makes sense and you wonder why the fuck mathfags have to make it sound so complicated.
 >> Anonymous Thu Jun 25 06:45:30 2020 No.11835147 >>11835142>What you wrote down is a tuple, up to embedding.>Which means it does not carry the "meta" information about it.in other words, it can be represented as an array, but it's not an array per se. that's what I've been saying the whole time.
 >> Anonymous Thu Jun 25 06:46:47 2020 No.11835149 >>11835145You have yet to define a difference other than the name, doesn't sound very scientific to me.
 >> Anonymous Thu Jun 25 06:47:33 2020 No.11835152 >>11835147Why did you say I was wrong and called me an idiot? In >>11835107.
 >> Anonymous Thu Jun 25 06:47:35 2020 No.11835153 File: 35 KB, 365x450, b005e4074bd5505f95dc2c2da1135d1c.jpg [View same] [iqdb] [saucenao] [google] [report] >boss asks you to code an infinite dimensional vector
 >> Anonymous Thu Jun 25 06:47:54 2020 No.11835154 >>11835152not me.
 >> Anonymous Thu Jun 25 06:49:03 2020 No.11835157 >>11835149An array can not be uniquely identified with a tensor. Neither can a tensor be uniquely identified with an array.>doesn't sound very scientific to me.Mathematics is not a science.
 >> Anonymous Thu Jun 25 06:49:59 2020 No.11835160 >>11834984Like this>int myArray[10][10][10]
 >> Anonymous Thu Jun 25 06:50:07 2020 No.11835162 >>11835145so i tell him it’s a tensor then it is the same as an array?btw isn’t this distinction literally the same as >>11835051?I really only wanted to know if I can represent every tensor as array in principle or if there are exceptions.
 >> Anonymous Thu Jun 25 06:50:44 2020 No.11835166 >>11835153let x = (1, 2, ..)This is valid Haskell by the way, there is no issue with representing infinite vectors.
 >> Anonymous Thu Jun 25 06:52:19 2020 No.11835169 >>11835157>They are not equalSo since it's not differentiable in code, show me in memory how it is different
 >> Anonymous Thu Jun 25 06:53:01 2020 No.11835172 >>11835146mostly to make the stuff as widely applicable as possible. shit’s defined in a way to be able to work with any abstract objects as long as they fulfill the necessary requirements.
 >> Anonymous Thu Jun 25 06:53:19 2020 No.11835173 File: 37 KB, 400x400, iZfir3BO_400x400.jpg [View same] [iqdb] [saucenao] [google] [report] >>11835166>boss asks you to take a fourier transform of that
 >> Anonymous Thu Jun 25 06:55:39 2020 No.11835176 >>11835169>>They are not equalWhere did I say that?>>11835169>So since it's not differentiable in codeA linear mapping is of type list of arithmetic type -> list of arithmetic type an array is of type list of list of arthimetic type.>show me in memory how it is differentLook at the type signatures? They will be stored with the data.
 >> Anonymous Thu Jun 25 06:57:14 2020 No.11835180 >>11835173Ask him for a better computer since it takes so long.Obviously you can write it down, it will just take an infinite amount of time...
 >> Anonymous Thu Jun 25 06:57:15 2020 No.11835181 >>11835162>btw isn’t this distinction literally the same as >>11835051 (You)?no, because the sets {maps V -> V} and {maps V* x V -> F} are isomorphic so-called naturally. the correspondence is cannonical, roughly in the sense that it doesn't require making any arbitrary choice along the way. on the other hand, representing a tensor as an array requires choice of a basis.in other words, if you ask two people to give you an array for a tensor, you will get two different answers and there's no reason to prefer one or the other. if you ask them to transform a map V->V into a map V*xV -> F you get the same answer.
 >> Anonymous Thu Jun 25 07:03:32 2020 No.11835192 >>11835162>so i tell him it’s a tensor then it is the same as an array?if you tell him it's a tensor, the type of the tensor, the vector space and the basis with respect to which is the tensor represented, ONLY then he can reconstruct the tensor.
 >> Anonymous Thu Jun 25 07:06:51 2020 No.11835197 >>11835162>really only wanted to know if I can represent every tensor as array in principleYou can literally represent every well-defined object as an array. You can represent this whole thread as just an array of numbers.
 >> Anonymous Thu Jun 25 07:09:42 2020 No.11835200 >>11835197>You can represent this whole thread as just an array of numbers.And in fact that is exactly what your computer is doing.
 >> Anonymous Thu Jun 25 07:10:58 2020 No.11835204 >>11835200Exactly.
 >> Anonymous Thu Jun 25 07:51:46 2020 No.11835248 >>11835197Yes, but is that an intuitive form of storage? The question is really more like "Is an array an intuitive way to represent tensors?".>>11835192What do you mean by type? The dimension and size? That should be implied in the array already. And the basis should also have an intuitive (obvious) representation as an array. I really don't see why you guys have a problem with this.
 >> Anonymous Thu Jun 25 08:32:19 2020 No.11835316 >>11835248>What do you mean by type?Have you not done any programming at all? How can you not know what a type is? At least on an intuitive basis everybody who has done the tiniest bit of programming should know about it.>The dimension and size?That is a small part of it, but not the most essential quality.>And the basis should also have an intuitive (obvious) representation as an array.Please, tell me an obvious representation of a basis for a Lebesgue space...>I really don't see why you guys have a problem with this.You seem to not understand extremely basic concenpts like a "type", of course then you can not understand the issue.
 >> Anonymous Thu Jun 25 08:34:26 2020 No.11835319 >>11835248>typegoogle what is (p,q)-tensor>And the basis should also have an intuitive (obvious) representation as an arrayalmost never does a space come with a preferred system of coordinates
 >> Anonymous Thu Jun 25 08:37:16 2020 No.11835325 >>11835181ok, but if I have a specific input and a specific transformation, the tensor will always be an array, right?
 >> Anonymous Thu Jun 25 08:40:05 2020 No.11835330 >>11835197give me a topology as array
 >> Anonymous Thu Jun 25 08:41:32 2020 No.11835333 >>11835330Which topology? I will give you the array that represents it.
 >> Anonymous Thu Jun 25 08:42:23 2020 No.11835336 >>11835325a tensor is represented by an array if bases of domain and codomain have been chosen. if there are no spaces, bases etc. (e.g. if you're just literally coding arrays as a way of storing numbers systematically without any relation to geometry), then you're not talking about tensors. maybe CSfags call it tensors, but it's simply wrong.
 >> Anonymous Thu Jun 25 08:43:43 2020 No.11835339 >>11835330If you can represent a space as an array, which you obviously can, then you can also represent the topology by an array.
 >> Anonymous Thu Jun 25 08:44:10 2020 No.11835341 >>11835333I want a donut cow plz
 >> Anonymous Thu Jun 25 08:47:04 2020 No.11835345 File: 25 KB, 500x500, B429C9DC-95B1-43F4-B11D-6856C42EC980.jpg [View same] [iqdb] [saucenao] [google] [report] >>11835336I think I get it now, thanks!
 >> Anonymous Thu Jun 25 08:47:45 2020 No.11835346 >>11831757What's the deal with the fucking dog shit kerning?
 >> Anonymous Thu Jun 25 08:52:05 2020 No.11835352 >>11835316I obviously know what a type in programming type is, but I thought we were talking about mathematical objects and not programming?
 >> Anonymous Thu Jun 25 09:12:48 2020 No.11835386 >>11835346What is kerning? Define it in C#. Is it some sort of array?
 >> Anonymous Thu Jun 25 09:19:32 2020 No.11835401 >>11835352>I thought we were talking about mathematical objects and not programming?Types encode the "meta" properties of an object. Both in a programming language and in mathematics. The programming concept originates in mathematics.>I obviously know what a type in programming typeThen you should know what the difference between a linear map and an array is.A linear map is a function, an array is data stored in a certain way.
 >> Anonymous Thu Jun 25 09:27:27 2020 No.11835419 >>11835336Okay but literally any quantity, to be represented in a computer, must implicitly be represented with the assumption of its field and vector space as well as magnitudes and units, for example a 3-dimensional velocity can only be encoded in a computer with the assumption of domain and codomain. And a 3-dimensional velocity is just an array, in terms of how it’s actually encoded, so a tensor is an array
 >> Anonymous Thu Jun 25 09:37:35 2020 No.11835459 >>11835419>must implicitly be represented with the assumption of its field and vector spaceNo. Of course not.The type is always explicitly associated with the data, that is the only way a computer would know what to do with it.>for example a 3-dimensional velocity can only be encoded in a computer with the assumption of domain and codomainBut the domain (which is part of its type) has to be *explicitly* stored.>And a 3-dimensional velocity is just an array, in terms of how it’s actually encodedNo. They have cleary different types and types are stored, well, at least the compiler uses the types to create a correct program where each object is associated with its correct type.
 >> Anonymous Thu Jun 25 09:47:28 2020 No.11835486 >>11835419Youre a moron.
 >> Anonymous Thu Jun 25 09:47:34 2020 No.11835487 >>11835459So, a tensor is just a specific type of array?
 >> Anonymous Thu Jun 25 09:53:19 2020 No.11835506 >>11835419for the hundredth time, yes, a tensor can be represented by an array. and for the hundredth time, no, that doesn't mean a tensor IS an array.
 >> Anonymous Thu Jun 25 09:55:25 2020 No.11835514 >>11835487>So, a tensor is just a specific type of array?What? No! How can you even read that from what I said?They are fundamentally different. Like a function and a list in a computer programm are fundamentally different.
 >> Anonymous Thu Jun 25 10:00:33 2020 No.11835528 >>11835487jfl
 >> Anonymous Thu Jun 25 15:34:20 2020 No.11836722 >>11835487Specifically it is an array of arrays.
 >> Anonymous Thu Jun 25 15:41:31 2020 No.11836739 File: 90 KB, 800x582, concept-programmer-hacker-cyberspace-manâ€™s-face-programming-code-background-programmer-144002238.jpg [View same] [iqdb] [saucenao] [google] [report] >>11831690 Tensors are gay.LIKE YOU!!!!!!!!!!
 >> Anonymous Thu Jun 25 15:41:49 2020 No.11836741 It's literally just an array of numbers. That's it.>but it could be an array of arraysThose are implemented in ram as just an array of numbers.>but I multiplied my array by a matrix, doesn't that make it special?No, it's just a fucking array. The way you use your array doesn't change what it is.
 >> Anonymous Thu Jun 25 15:48:18 2020 No.11836767 >>11836741Read the thread before posting, moron.
 >> Anonymous Thu Jun 25 15:55:38 2020 No.11836789 File: 14 KB, 236x274, 1592602381095.jpg [View same] [iqdb] [saucenao] [google] [report] >>11832366>multilinear algebrado people actually do this?
 >> Anonymous Thu Jun 25 15:55:55 2020 No.11836790 >>11836741brainlet
 >> Anonymous Thu Jun 25 16:01:00 2020 No.11836801 >>11836789Tensors are literally the thing that transforms "multilinear algebra" into plain old linear algebra. That's the whole point.When you have a multilinear functionf(x_1, ..., x_n) : V^n -> W for some vector space W, i.e. linear in each argument, you can uniquely characterize it as a linear function f: V tensor^n V -> W, where now the domain is a vector space instead of a set theoretic thingy.
 >> Anonymous Thu Jun 25 16:05:21 2020 No.11836818 File: 9 KB, 367x124, tensor.png [View same] [iqdb] [saucenao] [google] [report] i dunno guys, looks like an array of numbers to me!
 >> Anonymous Fri Jun 26 01:57:59 2020 No.11838332 >>11834012wait sorry, what's a vector?
 >> Anonymous Fri Jun 26 02:24:45 2020 No.11838394 >>11838332V is naturally isomorphic to {maps V* -> F}. At least if it's finite dimensional.
 >> Anonymous Fri Jun 26 02:34:21 2020 No.11838410 >>11836801Can you expand that into some sort of array?
 >> Anonymous Fri Jun 26 03:18:14 2020 No.11838508 >>11835107This gif saves the thread
 >> Anonymous Fri Jun 26 03:22:37 2020 No.11838513 >>11835152I was mocking the people who say mathematical structures are just arrays of numbers. If that were the case, you would be able to tell from my array of numbers that the object is a certain polynomial. Obviously you couldn't, because polynomials aren't just arrays of numbers, nor are vectors and tensors.
 >> Anonymous Fri Jun 26 04:48:54 2020 No.11838675 >>11838513>Obviously you couldn'tBut my answer was still 100% correct.
 >> Anonymous Fri Jun 26 05:31:54 2020 No.11838743 >>11831757Imagine have x y z for positions as values. Fucking shit dev make it an array of arrays.
 >> Anonymous Fri Jun 26 05:35:19 2020 No.11838746 >>11834984With an array of numbers
 >> Anonymous Fri Jun 26 06:29:53 2020 No.11838814 >>11831690A Tnesor is a multilinear mapping.Sometimes (more often than not) it CAN be represented in "multidimensional matrix form" if a basis is known, finite or at least countable.Then you can put it into a multi layered array in for example C#
 >> Anonymous Fri Jun 26 06:45:16 2020 No.11838846 >>11835160>myno its not. fuck off, control freak.
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