[pmoriarty]

"Tensor does imply a set of operations that are expected. Multiplying two arrays together is an ambiguous operation; multiplying two tensors together is well-defined."

In programming too, multiplying two arrays of arbitrary types is often undefined, and many languages allow their programmers to specify what they want to happen when arrays of specific types are multiplied (or may have built-in defined behavior for certain specific types of arrays).

I'd love to learn if there are any actual differences between tensors and arrays commonly used in programming, but so far it doesn't sound like it from reading through this HN thread.

[OkayPhysicist]

I think you misunderstood what I meant. If I say "multiply this 3x3 matrix by this 3x1 vector", then I know know to expect the particular form of multiplication that multiplies each column of the matrix by it's associated value in the vector, then adds them up to produce a 3x1 vector. Likewise, multiplying a 3x3x3 tensor by a 3x1x1 tensor will produce a 3x3x1 result.

If I say "multiply this 3x3 array by this 3x3 array", then it's an ambiguous operation. There is not a canonical multiplication for arrays. One ecosystem might treat it as a matrix-matrix multiplication, another might do an element-wise multiplication, others might just throw an error. None is more correct than another, because array just implies the structure of the data.