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Theory Manual Version 3.6
 Subsection A.1.8: Transpose of a Tensor Up Section A.1: Second-Order Tensors Subsection A.1.10: Determinant of a Tensor 

A.1.9 Double Product of Tensors

The double product of tensors is analogous to the dot product of vectors. Given two tensors and , the double product (or double contraction) is defined as Thus, for any tensor , . In component form, The double product of second order tensors is commutative.
Show that and .
Using indicial notation, and
 Subsection A.1.8: Transpose of a Tensor Up Section A.1: Second-Order Tensors Subsection A.1.10: Determinant of a Tensor