Tensor Operation And Quasi Congruent Standard Form

The product plays an important role in the study of tensors. Because of the complexity oftensors, calculations starting from the tensor’s definition are inconvenient. A variety of tensorproducts and some related properties are introduced, but the positive of tensors and thecorresponding quartic-form is inconsistent. So recursion algorithm about the product betweentensors and matrices is proposed in this paper. Especially, this algorithm is applied to discuss therelated operation of the fourth-order tensors. Finally, a congruent standard form ofbinary-quartic-form is achieved, so as to provide a judging theorem for the positive of the orderfour dimension two tensors.