Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New classes of matrix decompositions   The idea of decomposing a matrix into a product of structured matrices such
as triangular, orthogonal, diagonal matrices is a milestone of numerical
computations. In this paper, we describe six new classes of matrix
decompositions, extending our work in arXiv:1307.5132. We prove that every
$n\times n$ matrix is a product of finitely many bidiagonal, skew symmetric
(when n is even), generic, companion matrices and generalized Vandermonde
matrices, respectively. We also prove that a generic $n\times n$
centrosymmetric matrix is a product of finitely many symmetric Toeplitz (resp.
persymmetric Hankel) matrices. We determine an upper bound of the number of
structured matrices needed to decompose a matrix for each case.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin