Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subsequences of frames   Every frame in Hilbert space contains a subsequence equivalent to an
orthogonal basis. If a frame is n-dimensional then this subsequence has length
(1 - \epsilon) n. On the other hand, there is a frame which does not contain
bases with brackets.

4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ