If you have read the novel Cien Anos de Soledad and I told you that the gypsies wanted to sell you Tensors, I might get you to laugh a little bit. As the story progresses, we see that the leader of the gypsies, Melquiades, is a source of wisdom. So, how would the Gypsies sell us tensors?
They will hand us literature telling us why tensors are helpful and where they are used.
Then, speaking to us, they will tell us that a tensor lets us build a new math object from an old math object in a way that allows each component of the new object to be affected by every component of the old object. This is why you will buy tensors from the gypsies.
The variable x’ is influenced by both x and y in separate terms of a summation. Likewise for y’.
Ok, what if we have an old 2×2 matrix and we want to create a new 2×2 matrix?
We will need a tensor with 16 components so that each of the four components in the new matrix can be affected by each of the four components in the old matrix.
The image for this document abstractly shows a rank 4 tensor operating on an old 2×2 matrix to produce a new 2×2 matrix. The coordinates of a component tell the story of what it does. For example, 
Vectoreverything 