Related papers: On fully real eigenconfigurations of tensors

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

We show that Killing tensors on conformally flat $n$-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic…

For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on…

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also…

Let T be a general complex tensor of format $(n_1,...,n_d)$. When the fraction $\prod_in_i/[1+\sum_i(n_i-1)]$ is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T has finitely many minimal…

A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…

The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic…

We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary…

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different…

We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…

In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…

In this work we study different notions of ranks and approximation of tensors. We consider the tensor rank, the nuclear rank and we introduce the notion of symmetric decomposable rank, a notion of rank defined only on symmetric tensors. We…

Over a field of characteristic zero, we prove that for each r, there exists a constant C(r) so that the prime ideal of the rth secant variety of any Veronese embedding of any projective space is generated by polynomials of degree at most…

In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…

In this paper we study invariant local operations that can performed on a Fedosov manifold, with a particular emphasis on tensor-valued operations (also known as natural tensors). Our main result describes the spaces of homogeneous natural…

We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\geq3$ as well as those of Moore spaces. For $n>k\geq 3,$ we construct a finitely generated group defined by explicit generators and relations,…

Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic…

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…

Here, using two real non-zero parameters $\lambda$ and $\mu$, we construct Gaussian pseudo-orthogonal ensembles of a large number $N$ of $n \times n$ ($n$ even and large) real pseudo-symmetric matrices under the metric $\eta$ using $…