[akasakahakada]

Tensor product is basically the mathematical way to express if condition.

Say you have 2x2 matrix A, B, C.

Any arbitrary component within the Tensor(A, B, C) is:

  if A =(a1,a2) and B=(b1,b2) and C=(c1,c2): this value

The coordination is concatenation of matching dimension: (a1b1c1, a2b2c2)

While in many computational natural science, people using tensor product to store and manipulate data. Also it is how the mathematical equations being written on paper.

But in computer science's perspective, dealing with tensor matrix is simply a waste of memory since 90% of the time people are dealing with sparse system. System that their matrix is dominated by zero. Also it would be super clear if people just write if-then pseudocode instead of cryptic half-bake tensor expressions. People tend to invent their own notation while writting paper.

[consilient]

> Tensor product is basically the mathematical way to express if condition.

Not really, no. The way mathematicians actually express if conditions is with the word "if". The obvious pointlessly formal way to do it is with a pair of functions `ThingConditionedOn -> {0, 1}` and `{0, 1} -> Result`, but why would you?

> dealing with tensor matrix is simply a waste of memory since 90% of the time people are dealing with sparse system.

Tensors are not their components, any more than locations are their coordinates. Whether you choose a sparse or dense (or symbolic) encoding does not change the object being encoded.

[akasakahakada]

> encoding does not change the object being encoded

Here I am talking about real memory space. There exist more efficient isometrical representation of the same object but since mathematicians don't usually know computer, inefficient tensor matrix is by default. That's the problem.