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Theory Manual Version 3.6
 Subsection A.1.7: Identity Tensor and Tensor Inverse Up Section A.1: Second-Order Tensors Subsection A.1.9: Double Product of Tensors 

A.1.8 Transpose of a Tensor

Given a tensor , its transpose is denoted by which is defined by In component form, Also note that and and .
 Subsection A.1.7: Identity Tensor and Tensor Inverse Up Section A.1: Second-Order Tensors Subsection A.1.9: Double Product of Tensors