Isotropic Super-symmetric Tensors And Eigenvalues Of General Real Tensors

Tensor analysis is an important tool in theoretical physics, continuum mechanicsand many other areas of science and engineering. The paper mainly investigated theisotropic super-symmetric Descartes tensor, the eigenvalues of super-symmetric tensorand its characteristic polynomial and super-determinant of super-symmetric tensor. Thefull text is divided into six parts.The first part briefly introduce the research background and current situation ofthe tensor, and point out the main content of the paper. The second part introduces thebasic concepts of tensor.The third part consider the isotropic super-symmetric Descartestensor. At first, we introduce coordinate transformations and some conclusions, and thusdeduce the expression of isotropic super-symmetric Descartes tensor from second-orderto sixth-order.The fourth part mainly consider the symmetry of the super-symmetric tensor de-terminant. This part bases the study of the nature of symmetry super-determinantresultant.The fifth part studies the eigenvalue problem of the general real tensor eigen-values and E-characteristic values. And we give a positive answer in the literatureQi [24] of Question2.The sixth part is the Conclusion. This part summarizes the essayand makes a vision of the future.