  Complexity is an interdisciplinary concept which, first of all, addresses the
question of how order emerges out of randomness. For many reasons matrices
provide a very practical and powerful tool in approaching and quantifying the
related characteristics. Based on several natural complex dynamical systems,
like the strongly interacting quantum many-body systems, the human brain and
the financial markets, by relating empirical observations to the random matrix
theory and quantifying deviations in term of a reduced dimensionality, we
present arguments in favour of the statement that complexity is a pheomenon at
the edge between collectivity and chaos.
