Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $p$-norm of circulant matrices   In this note we study the induced $p$-norm of circulant matrices $A(n,\pm a,
b)$, acting as operators on the Euclidean space $\mathbb{R}^n$. For circulant
matrices whose entries are nonnegative real numbers, in particular for
$A(n,a,b)$, we provide an explicit formula for the $p$-norm, $1 \leq p \leq
\infty$. The calculation for $A(n,-a,b)$ is more complex. The 2-norm is
precisely determined. As for the other values of $p$, two different categories
of upper and lower bounds are obtained. These bounds are optimal at the end
points (i.e. $p=1$ and $p = \infty$) as well as at $p=2$.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio