Tensor & Matrix: Cartesian Vector & Transformation Rule?

[hokhani]

Each set of constant numbers such as $(v_1, v_2, v_3)$ are the components of a constant Cartesian vector because by rotation of coordinates they satisfy the transformation rule. Can we consider each set of constant arrays $a_{ij};i,j=1,2,3$ as components of a Cartesian tensor? In other words, does each set of this type satisfy the tensor transformation rule?

 

[andrewkirk]

What do you mean by a Cartesian tensor? Cartesian is usually used to refer to a coordinate system, not a tensor, or a vector, both of which are coordinate-independent objects.
Given any 3 x 3 Cartesian coordinate system, the matrix you mention will be the representation in that coordinate system of a tensor.

 

[hokhani]

What do you mean by a Cartesian tensor? Cartesian is usually used to refer to a coordinate system, not a tensor, or a vector, both of which are coordinate-independent objects.
Given any 3 x 3 Cartesian coordinate system, the matrix you mention will be the representation in that coordinate system of a tensor.

Thanks. By "Cartesian tensor" I meant the representation of a tensor in Cartesian coordinate system.