Title: Inertia, positive definiteness and $\ell_p$ norm of GCD and LCM matrices and their unitary analogs,
Abstract: Let $S=\{x_1,x_2,\dots,x_n\}$ be a set of distinct positive integers, and let
$f$ be an arithmetical function. The GCD matrix $(S)_f$ on $S$ associated with
$f$ is defined as the $n\times n$ matrix having $f$ evaluated at the greatest
common divisor of $x_i$ and $x_j$ as its $ij$ entry. The LCM matrix $[S]_f$ is
defined similarly. We consider inertia, positive definiteness and $\ell_p$ norm
of GCD and LCM matrices and their unitary analogs. Proofs are based on matrix
factorizations and convolutions of arithmetical functions.