  This paper has aim to characterize Fredholmness and Weylness of upper
triangular operator matrices having arbitrary dimension n. We present various
characterization results in the setting of infinite dimensional Hilbert spaces,
thus extending some known results from Cao X. et al. (2006, 2005) and Zhang et
al. (2012) to the case of arbitrary dimension n. We pose our results without
using separability assumption, thus improving perturbation results from Wu X.
et al. (2020).
