Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum relative distance between symmetric rank-two and rank-one
  tensors   It is shown that the relative distance in Frobenius norm of a real symmetric
order-$d$ tensor of rank two to its best rank-one approximation is upper
bounded by $\sqrt{1-(1-1/d)^{d-1}}$. This is achieved by determining the
minimal possible ratio between spectral and Frobenius norm for symmetric
tensors of border rank two, which equals $\left(1-{1}/{d}\right)^{(d-1)/{2}}$.
These bounds are also verified for nonsymmetric tensors of order $d=3$.

32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio