Border Rank Nonadditivity for Higher Order Tensors
نویسندگان
چکیده
Whereas matrix rank is additive under direct sum, in 1981 Sch\"onhage showed that one of its generalizations to the tensor setting, border rank, can be strictly subadditive for tensors order three. Whether higher has remained open. In this work, we settle problem by providing analogs Sch\"onhage's construction four and higher. work was motivated study computational complexity multiplication; discuss implications our results asymptotic multiplication tensor.
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2021
ISSN: ['1095-7162', '0895-4798']
DOI: https://doi.org/10.1137/20m1357366