Related papers: Natural symmetric tensor norms

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…

This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms,…

We prove that a nonsymmetric normal entry pattern of order $n$ ($n\ge 3$) has at most $n(n-3)/2+3$ distinct indeterminates and up to permutation similarity this number is attained by a unique pattern which is explicitly described.

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are…

We study typical ranks with respect to a real variety $X$. Examples of such are tensor rank ($X$ is the Segre variety) and symmetric tensor rank ($X$ is the Veronese variety). We show that any rank between the minimal typical rank and the…

In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization…

We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field --- the value of the nuclear norm of a…

We show that the spectral norm of a $d$-mode real or complex symmetric tensor in $n$ variables can be computed by finding the fixed points of the corresponding polynomial map. For a generic complex symmetric tensor the number of fixed…

This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…

We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the free associative algebra vanishes as well in any n-generated…

The totally-real embeddability of any $2k$-dimensional compact manifold $M$ into $\mathbb C^n$, $n\geq 3k$, has several consequences: the genericity of polynomially convex embeddings of $M$ into $\mathbb C^n$, the existence of $n$ smooth…

We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of…

In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order n $\ge$ 1. These conditions are effective and of degree…

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…

It is conjectured since long that for any convex body $P\subset \mathbb{R}^n$ there exists a point in its interior which belongs to at least $2n$ normals from different points on the boundary of $P$. The conjecture is known to be true for…

We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…

We define a 3-algebra with structure constants being symmetric in the first two indices. We also introduce an invariant anti-symmetric tensor into this 3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal…

We give a new approach to the symmetries of the Painlev\'e equations $P_{V},P_{IV},P_{III}$ and $P_{II}$, respectively. Moreover, we make natural extensions to fourth-order analogues for each of the Painlev\'e equations $P_{V}$ and…

The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order tensor is equal to the square root of the spectral norm of…