Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal Decomposition of Symmetric Tensors   A real symmetric tensor is orthogonally decomposable (or odeco) if it can be
written as a linear combination of symmetric powers of $n$ vectors which form
an orthonormal basis of $\mathbb R^n$. Motivated by the spectral theorem for
real symmetric matrices, we study the properties of odeco tensors. We give a
formula for all of the eigenvectors of an odeco tensor. Moreover, we formulate
a set of polynomial equations that vanish on the odeco variety and we
conjecture that these polynomials generate its prime ideal. We prove this
conjecture in some cases and give strong evidence for its overall correctness.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc