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[–] 56 points 1 year ago (1 child)

To approach from another angle...

Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices.

https://mathworld.wolfram.com/Tensor.html

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  • [–] 32 points 1 year ago* (5 children)

    Avengers Endgame is just a stream of numbers

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  • [–] 17 points 1 year ago (4 children)

    All of creation is just a stream of numbers

    And we call that physics

    And that is beautiful

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  • [–] 28 points 1 year ago* (last edited 1 year ago) (1 child)

    Excuse me, but a tensor is actually a blob of numbers which extends the concept of a matrix to a generic sequence and stride data structure.

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  • [–] 13 points 1 year ago (1 child)

    You really did a number on this one

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  • [–] 13 points 1 year ago

    A tensor is one that transforms like a tensor 🤯

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  • [–] 12 points 1 year ago

    Can you all keep it down! You’re mathing too loudly for this time of night. Some of us have to get up early(ish).

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  • [–] 12 points 1 year ago

    You're quite a number bee hat tip emoji

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  • But a grid can just be a number with a list of numbers. A tensor is just two numbers with a list of numbers. A n-tensor is just two lists of numbers. Two lists can be combined with a number to indicate when they split. If we put that number at the start of the list, then we just have a list.

    Everything is just a list of numbers.

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  • [–] 9 points 1 year ago

    I am THE NUMBER

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  • [–] 8 points 1 year ago

    A scalar is just a 0th order tensor

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  • [–] 7 points 1 year ago

    a tensor is just an element of a tensor product. and a tensor product is just a way to multiply algebraic structures

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  • [–] 7 points 1 year ago (1 child)

    A number is just a type of vector

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  • [–] 7 points 1 year ago (6 children)

    A tensor is a special box of numbers that doesn't change under coordinate transformation.

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  • [–] 3 points 1 year ago

    Which is really a roundabout way of saying a tensor is a multilinear relationship between arbitrary products of vectors and covectors. They're inherently geometric objects that don't depend on a choice of coordinate system. The box of numbers is just one way of looking at a tensor, like a matrix is to a linear transformation on a vector space

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  • [–] 4 points 1 year ago (2 children)

    Where does this definition come from?

    All the geometric definitions of tensors I have met always assumed a base, such that a change of coordinate or of parametrization would change the values of the tensor. Unless you define the tensor by its action instead of its values?

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  • [–] 4 points 1 year ago

    That's exactly correct. It's similar to how a vector in R^2 is just an arrow with a magnitude and a direction. When you represent that arrow in different bases, the arrow itself isn't changing, just the list of numbers you use to represent them. Likewise, tensors do not change when you change bases, but their representations as n dimensional grids of numbers do change.

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  • [–] 6 points 1 year ago (3 children)

    A Pi is just an endless string of numbers.

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  • [–] 6 points 1 year ago (2 children)

    Hnghhhhh I can't agree. Its decimal representation is an endless string of digits, yes. However, in base π, π is represented by only one digit.

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  • [–] 5 points 1 year ago

    And this is the reason why no one knows what a tensor is. (This also completely blows up in your face as soon as you have infinite dimensions)

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  • [–] 3 points 1 year ago

    These collections also happen to follow a few specific geometric rules.

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  • [–] 3 points 1 year ago

    Math is just syntax.

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  • [–] 3 points 1 year ago (6 children)

    I mean... it also has to be linear too, but sure okay ☺️

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  • [–] 8 points 1 year ago (1 child)

    What has to be linear? Vector?matrix? Tensor? Neither makes sense

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  • [–] 5 points 1 year ago

    You lost me at vectors not having to be linear. You can apply nonlinear functions or operations to vectors, but doing so transforms them into a different, non-linear context, afaik. We might be using different definitions of some of these terms, especially "linear".

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  • [–] 1 point 1 year ago* (3 children)

    "Linear" describes transformations, not numbers.

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  • [–] 3 points 1 year ago (2 children)

    Isn't a tensor a multilinear map taking as input a tensor and outputting another tensor?

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  • [–] 2 points 1 year ago

    You just used "tensor" to define "tensor," but also any list of number formulated as an n-dimensional matrix will satisfy this criterion. A tensor is both a linear transformation and an n-dimensional box-shaped list of numbers, but there's nothing such as a linear list of numbers.

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  • Overly simplified math meme is bad. Take it down

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