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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Acknowledgements
This research was done within the activities of the Centro de Estruturas Lineares e Combinatórias (CELC) and was supported by Fundação para a Ciência e a Tecnologia (FCT). The work of R. Simões was also supported by CELC grant BIC-CI/04/00, during 2000/2001 and FCT grant SFRH/BM/4422/2001, during 2001/2002.