>>13850754A tensor in the context of a finite dimensional vecotor space can, just as a regular vector. be represented as a list of numbers, however, that is just a representation in a particular basis.
Just like how a vector can be represented with many lists of numbers depending on the basis vectors, so can tensors.
A physicist will tell you a tensor is simply a mathematical object that when you change coordinates (and hence the natrual basis) the object is "invariant", what that essentially means is that there is something inherently geometric about the object that does NOT depend on your frame of refrence.
A mathematican will likely tell you that a tensor is a multilinear map from the tangent and cotangent space of a manifold to the scalar field. From this definition the array and transformation properties can be deduced. This definition is ok for finitie dimensional vector spaces, and particularly for the tangent space of a manifold, it doesn't generalise to infinite dimensional vector spaces however, althuogh that is not necessary when first learning about tensors.
