It is correct to say that a tensor is simply a multidimensional array of related quantities?
More specifically a tensor is a collection or tuples of vectors where every vector in the tuple represent a different type of information but the components of the different vectors depend of each other.
I said this because of the following sentence I read in Wikipedia:
"at the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in spacetime"
I understand that electric and magnetic fields are grouped into a tensor because the components the magnetic field depend of some maner of the components of the electric field and viceversa.
But what about tensors as transformation objects? if you have two vectors (not tuples of vectors) then the transformation is simply a matrix (or rank 2 tensor), but what is the necessity for tensors of rank bigger than 2? Is to transform tuples of vectors?
I only have a background in physics so please try to answer in the most simple terms.