Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal forms of endomorphism-valued power series   We show for $n,k\geq1$, and an $n$-dimensional complex vector space $V$ that
if an element $A\in\text{End}(V)[[z]]$ has constant term similar to a Jordan
block, then there exists a polynomial gauge transformation $g$ such that the
first $k$ coefficients of $gAg^{-1}$ have a controlled normal form.
Furthermore, we show that this normal form is unique by demonstrating explicit
relationships between the first $nk$ coefficients of the Puiseux series
expansion of the eigenvalues of $A$ and the entries of the first $k$
coefficients of $gAg^{-1}$.

26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org