We have studied small carbon molecules using a matrix-isolation technique. Our experimental setup is described in detail. The carbon clusters were produced by evaporating graphite and trapping the carbon-vapor molecules in solid argon, where molecular growth could be induced by controlled matrix annealing. To identify the produced molecules, absorption spectroscopy in the ultraviolet (UV)-visible and infrared (IR) spectral ranges was applied. Additional characterization of the excited and ground states of the molecules was obtained from emission and excitation spectra. The molecules were excited by a pulsed dye laser system and the emission spectra were recorded with a high-sensitivity photodiode-array spectrometer. We present our measurements on linear C-3. The (A) over tilde (IIu)-I-1 excited state of linear C-3 was populated by the electronic transition (A) over tilde (IIu <--)-I-1(X) over tilde (1)Sigma(g)(+), and the corresponding excitation spectra of the C-3 fluorescence ((A) over tilde (IIu)-I-1 -->(X) over tilde (1)Sigma(g)(+)) and phosphorescence ((a) over tilde (IIu)-I-3-->(X) over tilde (1)Sigma(g)(+)) were studied. Comparison of excitation and absorption spectra yielded information on site effects due to the matrix environment. Emission bands in the fluorescence and phosphorescence spectra up to vibrational energies of 8500 cm(-1) could be observed. The radiation lifetime of the (A) over tilde (IIu)-I-1 excited state of C-3 in solid argon was found to be shorter than 10 ns. The phosphorescence transition (a) over tilde (3)IIu-->(X) over tilde (1)Sigma(g)(+) decays in about Id ms and its rise indicates fast vibrational relaxation within the triplet system. Our data support a linear ground state geometry for C3 also in solid argon.