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?
I'm asking several things: i) It is correct to say that a tensor as a quantity is a tuple of vectors, that is needed to group vectors of different types that are related like the magnetic and electric fields ii) Can a tensor by viewed as linear transformation? In this sense how a tensor is different from a regular matrix? It is because it transform tuples of vectors instead of simple vectors? iii) What is an example of a tensor as a linear transformation in physics?