Simplicity and typical rank of three‐way arrays, with applications to Tucker‐3 analysis with simple cores

In chemometric applications of Tucker three‐way principal component analysis, core arrays are often constrained to have a large majority of zero elements. This gives rise to questions of non‐triviality (are the constraints active, or can any core of a given format be transformed to satisfy the constraints?) and uniqueness (can we transform the components in one or more directions without losing the given pattern of zero elements in the core?). Rather than deciding such questions on an ad hoc basis, general principles are to be preferred. This paper gives an overview of simplicity transformations on the one hand, and typical rank results on the other, which are suitable to determine whether or not certain constrained cores are trivial.