Flags and equality of tensors

Equality of immanantal decomposable tensors, II

“…These conditions extend the above refereed conditions for ∧ m V and ∨ m V and can be viewed as a "mixture" of them. They also extend previous work done on this topic [7,4].…”

“…and, since T (R(D), 1) is an orthogonal projection, we get from (10) (using equalities (4) and (5)) the equality (T (R(D), 1)(u 1 ⊗ · · · ⊗ u m ), T (C(D), )(x 1 ⊗ · · · ⊗ x m )) = (T (R(D), 1)(u 1 ⊗ · · · ⊗ u m ), T (C(D), )(y 1 ⊗ · · · ⊗ y m )).…”

“…However, some partial results have appeared in recent years. The main theorem proved in [4] is a necessary and sufficient condition for equality of immanantal decomposable tensors x 1 * · · · * x m = y 1 * · · · * y m with the assumption that the rank partition of (x 1 , . .…”

Small perturbations and pairs of matrices that have the same immanent

“…, m À mÀ1 Þ is a partition of m À jL(M)j. This sequence is called the rank partition of M and it has been studied in several papers [2][3][4][5][8][9][10]20].…”

Equality of symmetrized tensors and the flag variety

“…(v 1 ⊗ · · · ⊗ v n )T λ = (u 1 ⊗ · · · ⊗ u n )T λ (1) was studied by Merris [12], and Chollet and Marcus [2,11] in the mid-1970s. Since then, many papers were written on this question and partial results were given by a variety of authors over the years (for example, [3,6,7,8,9]). However, the question was fully resolved only recently in two papers by da Cruz and Dias da Silva [4,5].…”