# What is a tensor?

I'm trying to understand a paper that works with tensors. I understand that a tensor of rank 0 is a scalar, a tensor of rank 1 is a vector, and a tensor of rank 2 is a dyad (and therefore it can be considered a matrix, correct me if I'm wrong).

The paper that I am trying to work with is using a rank 3 (i am not sure if it is the rank if someone could explain deeply what's the rank I would be grateful). What I mean by rank three is that has $$m*n*z$$, that's the image I have about the tensor of rank 3:

I would like to know if a rank 3 tensor would look like the one in the photo, I imagine it looks like a 3-D matrix, am I right?

Also, if someone could explain how to calculate the rank of a tensor I would pretty much appreciate it.

• This question might be a bit too broad. What field are you studying this in relation to? And yes, if you have a rank $n$ tensor, you can imagine it as a grid of numbers fitting within an $n$-cube (or rectangular object), but without knowing how it is used, it's not that useful of a description. – Joppy Oct 5 '18 at 9:35
• math/computer science has a different notion of a tensor than physics. In the first definition, it's just $n$-dimensional array (grid of numbers, possibly with different number of elements in each directions). So you need $n$ indexes to refer to an element. In physics, it's called a tensor only if it represents a physical property (and therefore transforms correctly under coordinate change). See this: math.stackexchange.com/questions/757351/… – orion Oct 5 '18 at 11:28
• We see such questions here time and again. See, e.g., the following: math.stackexchange.com/questions/657494/… – Christian Blatter Oct 5 '18 at 15:54