Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalization of the Brauer Theorem to Matrix Polynomials and Matrix
  Laurent Series   Given a square matrix $A$, Brauer's theorem [Duke Math. J. 19 (1952), 75--91]
shows how to modify one single eigenvalue of $A$ via a rank-one perturbation,
without changing any of the remaining eigenvalues. We reformulate Brauer's
theorem in functional form and provide extensions to matrix polynomials and to
matrix Laurent series $A(z)$ together with generalizations to shifting a set of
eigenvalues. We provide conditions under which the modified function
$\widetilde A(z)$ has a canonical factorization $\widetilde A(z)=\widetilde
U(z)\widetilde L(z^{-1})$ and we provide explicit expressions of the factors
$\widetilde U(z)$ and $\widetilde L(z)$. Similar conditions and expressions are
given for the factorization of $\widetilde A(z^{-1})$. Some applications are
discussed.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio