Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Angles between subspaces and their tangents   Principal angles between subspaces (PABS) (also called canonical angles)
serve as a classical tool in mathematics, statistics, and applications, e.g.,
data mining. Traditionally, PABS are introduced via their cosines. The cosines
and sines of PABS are commonly defined using the singular value decomposition.
We utilize the same idea for the tangents, i.e., explicitly construct matrices,
such that their singular values are equal to the tangents of PABS, using
several approaches: orthonormal and non-orthonormal bases for subspaces, as
well as projectors. Such a construction has applications, e.g., in analysis of
convergence of subspace iterations for eigenvalue problems.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio