Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New multiplicative perturbation bounds for the generalized polar
  decomposition   Some new Frobenius norm bounds of the unique solution to certain structured
Sylvester equation are derived. Based on the derived norm upper bounds, new
multiplicative perturbation bounds are provided both for subunitary polar
factors and positive semi-definite polar factors. Some previous results are
then improved.

34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio