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.