This is a further discussion of a previous work of the author on tensors with different rank and
symmetric rank. We point out several obstructions towards extending a complex number …

Tensor decompositions have become essential tools for feature extraction and compression
of multiway data. Recent advances in tensor operators have enabled desirable properties of …

Matrices can be decomposed via rank-one approximations: the best rank-one approximation
is a singular vector pair, and the singular value decomposition writes a matrix as a sum of …

Firstly, we propose an algebraic method to compute the symmetric rank and symmetric rank
decomposition for symmetric tensors over the binary field, when the order is at least the …

This thesis explores two distinct subjects at the intersection of commutative algebra,
algebraic geometry, multilinear algebra, and computer-aided geometric design: 1. The study …

Shitov recently gave counterexamples over the real and complex field to Comon's
conjecture that the symmetric tensor rank and tensor rank of a symmetric tensor are the …

Using methods of Part I, we build a symmetric tensor whose rank differs from the symmetric
rank, for any infinite field F with char F= 2, 3. Part I of this series [47] gives a detailed …

These notes are intended to be up-to-date compared to previous similar lecture notes, like
[CGO14], including references from the last decade, but at the same time they offer only a …

This is a refutation of an earlier conjecture of the author.... всё, что неровно лежит. Detsl
aka Le Truk, Пробки, стройка, грязь The nature of the contemporary peer review system …