Thanks. By "Cartesian tensor" I meant the representation of a tensor in Cartesian coordinate system.andrewkirk said: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.
A tensor is a mathematical object that describes the relationships between multiple vectors and scalars in a coordinate-independent manner. It can be thought of as a generalization of a vector or matrix to higher dimensions.
A tensor is a higher-dimensional object that can contain multiple vectors and scalars, while a matrix is a two-dimensional array that contains only numbers. Additionally, tensors follow different transformation rules than matrices.
A Cartesian vector is a vector that is defined in a specific Cartesian coordinate system. It has a magnitude and direction, and can be represented by an ordered set of numbers (coordinates) in the coordinate system.
The transformation rule for tensors states that the components of a tensor will transform according to a specific formula when the coordinate system is changed. This transformation rule ensures that the tensor remains invariant (unchanged) under different coordinate systems.
Tensors are used extensively in physics and engineering to describe physical quantities and their relationships. They are especially useful in fields such as mechanics, electromagnetism, and relativity where the laws of physics are described using tensors.