Tensor Is the Might

I know there are different contexts, but a tensor is not a collection of numbers, in a mathematical sense. A vector is not a list of numbers. Such collections of numbers are representations of objects with very specific kinds of properties under coordinate transformations.

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.

> A tensor is nothing but a flat array of numbers, plus some metadata telling you how to interpret those numbers as a multi-dimensional object.

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.

Yes, this is what I'm complaining about.

> coopt: to appropriate as one's own; preempt.

The term existed for some time before programming if that's your source of confusion. Now it is a twisted and ambiguous version of itself.