“…Therefore, a diagonal tensor S is not achievable, but we want to maximize its diagonal in a certain way. In papers [1,13,8,9] authors develop the Jacobi-type algorithms for maximizing the Frobenius norm of the diagonal of S, that is, maximizing the sum of the squares of the diagonal elements of S. Here, inspired by the algorithm of Moravitz Martin and Van Loan [10], we design a Jacobi-type algorithm that maximizes the trace of S. For a given tensor A ∈ R n×nו••×n we are looking for its decomposition of the form (1.1) such that tr(S) = Using the properties of the mode-m product one can express the core tensor S as…”