https://web.archive.org/web/20111015133833/http://www-staff....

This was used in his shape aware language FiSh, for dealing with multidimensional arrays. Shape compatibilities were statically type checked, if I recall correctly. Shapes were also used to optimize the loops.

[Programming in FISh] https://link.springer.com/article/10.1007/s100090050037

[Towards Dynamic Shaping] https://www.researchgate.net/publication/265975794_Towards_D...

Erm... many would disagree. I think what he means is just a multidimensional array.

I think it genuinely damages people's ability to digest the mathematics to tell them first and foremost that these objects are collections of numbers.

  {
      {user:bob, movie:"Heat"}:0.1,
      {user:alice, movie:"Frozen"}:0.9,
      {user:carol, movie:"Top Gun"}:0.3,
  }

Yikes! No.

I mean even for the intents and purposes of using this definition in ML, this might not be right.

I am trying not to be pedantic, so I will not go with the official/mathematical definition of a tensor as that could be incredibly confusing (look it up!!!).

But a tensor is a LOT more than that. Essentially it's a multilinear map that transforms a set of basis vectors in a certain way, and is coordinate agnostic.

This is not even half its definition so you can see how much the author left out.

Having said that, this is still a good way to start getting intuition into it and I urge the author to continue refining the definition as he/she learns more.

Disclaimer: MS in Math with concentration of GR.

EDIT: Also tensor aren't simply "flat" array of numbers. They are multidimensional. A grounded example, a rank 3 tensor is a collection of 2d matrices. Think of it as a bunch of 2d matrices stacked on top of each other. You need 3 indices to keep track of numbers --- sure in a programming language, it can be represented as a 1d array as well with 0s filling up empty spaces, but you get the idea.

I'm so very, very tired of tech coopting rigorous mathematical terms.