A series of cationic molecular fragments (C-n(+), n = 11, 12, 15, 16, 18, and 21), produced by electron-impact ionization of C-60 in the gas phase, were each mass-selected and accumulated in cryogenic Ne matrices. Optical absorption measurements in the UV-vis and IR spectral ranges reveal linear carbon chain structures. In particular, we have observed the known electronic transitions of linear C-11, C-15, and C-21. The NIR transitions of linear C-15(-),C-16(-), and C-18(-) have also been detected, indicating that soft-landing of the corresponding cations can also involve charge-changing. Newly observed electronic absorptions at 410.3 and 429.9 nm have been assigned to linear C-18 absorptions at 438.2, 443.5, 422.3, and 433.7 nm, to linear C-15(+), and absorption at 395.5 nm, to linear C-16. Increasing deposition energy leads to fragmentation upon impact. This is indicated by absorptions of C-10 (313, 316.3 nm), when depositing C-n(+), (n = 11, 15, 16) as well as C-12 (332 nm) or C-14 (347.4, 356.6 nm), when depositing C-15(+) or C-16(+), respectively. These were previously assigned to cyclic isomers. We reassign them to linear isomers here on the basis of plausibility arguments. The observations have been supported by time-dependent density functional theory calculations for ring and chain isomers of C-n(+/-), 10 <= n <= 20 up to the vacuum-UV range. The electronic absorptions of carbon chains are at least 1 order of magnitude stronger than all NIR electronic absorptions of C-60(+), which have recently been attributed to several of the diffuse interstellar bands. Considering that fullerene multifragmentation yields long carbon chains that have very strong absorptions both in the UV-vis and IR spectral regions, these systems appear to be good candidates to be observed in regions of space containing fullerenes.