Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The eigenvector-eigenvalue identity for the quaternion matrix with its
  algorithm and computer program   Peter Denton, Stephen Parker, Terence Tao and Xining Zhang [arxiv 2019]
presented a basic and important identity in linear commutative algebra,
so-called {\bf the eigenvector-eigenvalue identity} (formally named in [BAMS,
2021]), which is a convenient and powerful tool to succinctly determine
eigenvectors from eigenvalues. The identity relates the eigenvector component
to the eigenvalues of $A$ and the minor $M_j$, which is formulated in an
elegant form as \[ \lvert v_{i,j} \rvert^2\prod_{k=1;k\ne
i}^{n-1}({\lambda_i}(A)-{\lambda_k}(A))=\prod_{k=1}^{n-1}({\lambda_i}(A)-{\lambda_k}(M_j)).
\,\,\,%\mbox{(\cite{tao-eig,D-P-T-Z})} \]
  In fact, it has been widely applied in various fields such as numerical
linear algebra, random matrix theory, inverse eigenvalue problem, graph theory,
neutrino physics and so on. In this paper, we extend the eigenvector-eigenvalue
identity to the quaternion division ring, which is non-commutative. A version
of eigenvector-eigenvalue identity for the quaternion matrix is established.
Furthermore, we give a new method and algorithm to compute the eigenvectors
from the right eigenvalues for the quaternion Hermitian matrix. A program is
designed to realize the algorithm to compute the eigenvectors. An open problem
ends the paper. Some examples show a good performance of the algorithm and the
program.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio