Abstract
The concept of rank partition of a family of vectors v 1, … , vm is a generalization of that has been useful for studying problems in Multilinear Algebra, namely, establishing conditions for non-vanishing decomposable symmetrized tensors and conditions for the equality of decomposable symmetrized tensors. A previous paper has described the rank partitions that can be obtained with arbitrarily small perturbations of the vectors v 1, … , vm . The purpose of the present article is to describe the pairs of row rank partitions and column rank partitions that can be obtained with arbitrarily small perturbations of a matrix.
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