Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schmidt Representation of Bilinear Operators on Hilbert Spaces   Current work defines Schmidt representation of a bilinear operator $T: H_1
\times H_2 \rightarrow K$, where $H_1, H_2$ and $K$ are separable Hilbert
spaces. Introducing the concept of singular value and ordered singular value,
we prove that if $T$ is compact, and its singular values are ordered, then $T$
has a Schmidt representation on real Hilbert spaces. We prove that the
hypothesis of existence of ordered singular values is fundamental.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin