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Theory Manual Version 3.6
 Section A.1: Second-Order Tensors Up Section A.1: Second-Order Tensors Subsection A.1.2: Cartesian Components of a Tensor 

A.1.1 Definition

Let be a transformation, which transforms any vector into another vector, e.g., If has the following properties, where and are arbitrary vectors, and is an arbitrary scalar, then is called a linear transformation, a second-order tensor, or simply a tensor. Vectors are first-order tensors and scalars are zeroth-order tensors.
 Section A.1: Second-Order Tensors Up Section A.1: Second-Order Tensors Subsection A.1.2: Cartesian Components of a Tensor