Eigenvalues and invariants of tensors

摘要: Abstract A tensor is represented by a supermatrix under co-ordinate system. In this paper, we define E-eigenvalues and E-eigenvectors for tensors supermatrices. By the resultant theory, E-characteristic polynomial of tensor. An E-eigenvalue root polynomial. regular case, complex number an if only it We convert to monic show that coefficients are invariants tensor, i.e., they invariant system changes. call them principal The maximum mth order n-dimensional function m n. denote d ( , n ) 1 = 2 ⩾ 3 ⩽ − + ⋯ . also rank All real eigenvectors associated with nonzero in subspace dimension equal its rank.