Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerating partial linear transformations in a similarity class   Let $V$ be a finite-dimensional vector space over the finite field ${\mathbb
F}_q$ and suppose $W$ and $\widetilde{W}$ are subspaces of $V$. Two linear
transformations $T:W\to V$ and $\widetilde{T}:\widetilde{W}\to V$ are said to
be similar if there exists a linear isomorphism $S:V\to V$ with
$SW=\widetilde{W}$ such that $S\circ T=\widetilde{T}\circ S $. Given a linear
map $T$ defined on a subspace $W$ of $V$, we give an explicit formula for the
number of linear maps that are similar to $T$. Our results extend a theorem of
Philip Hall that settles the case $W=V$ where the above problem is equivalent
to counting the number of square matrices over ${\mathbb F}_q$ in a conjugacy
class.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys