But no need to get all worked up, because we’re going to break them down in the most casual way possible (because who wants math to be boring?).

Before anything else: what is a tensor product? Well, let’s start with tensors themselves they are mathematical objects that represent arrays of numbers or functions. They can have different dimensions and shapes, but for our purposes today we’re going to focus on two-dimensional tensors (also known as matrices).

Now, imagine you have two matrices: one is a 3×2 matrix called A, and the other is a 2×4 matrix called B. You want to multiply them together, but there’s a catch they don’t match up perfectly in terms of dimensions (A has more rows than columns compared to B).

This is where tensor products come in handy! By taking the tensor product of A and B, we can create a new matrix that has 3 times as many rows as A and 4 times as many columns as B. This allows us to multiply them together without any issues (assuming they have compatible dimensions).

But wait what about coordinate representations? Well, let’s say you have a vector in three-dimensional space: [1, 2, 3]. You want to represent this vector using coordinates on a plane. To do so, we can create two new vectors that are perpendicular to each other (let’s call them x and y).

Now, imagine projecting the original vector onto these new axes you get two numbers: one for how much of the original vector is in the direction of x, and another for how much of it is in the direction of y. These are called coordinates! By using coordinate representations, we can represent a vector in three-dimensional space as a pair of vectors (one for each axis) that live on a plane.

Who knew math could be so fun?