  Damped transverse oscillations of magnetic loops are routinely observed in
the solar corona. This phenomenon is interpreted as standing kink
magnetohydrodynamic waves, which are damped by resonant absorption owing to
plasma inhomogeneity across the magnetic field. The periods and damping times
of these oscillations can be used to probe the physical conditions of the
coronal medium. Some observations suggest that interaction between neighboring
oscillating loops in an active region may be important and can modify the
properties of the oscillations compared to those of an isolated loop. Here we
theoretically investigate resonantly damped transverse oscillations of
interacting non-uniform coronal loops. We provide a semi-analytic method, based
on the T-matrix theory of scattering, to compute the frequencies and damping
rates of collective oscillations of an arbitrary configuration of parallel
cylindrical loops. The effect of resonant damping is included in the T-matrix
scheme in the thin boundary approximation. Analytic and numerical results in
the specific case of two interacting loops are given as an application.
