where formula_6 is the "core tensor", a 3rd-order tensor that contains the 1-mode, 2-mode and 3-mode singular values of formula_7, which are defined as the "frobenius norm" of the 1-mode, 2-mode and 3-mode slices of tensor formula_8 respectively. formula_9 are unitary matrices in formula_10 respectively. the "j"-mode product ("j" = 1, 2, 3) of formula_11 by formula_12 is denoted as formula_13 with entries as