The quasi-block-stochastic
matrices are introduced as a generalization of the block-stochastic and the
quasi-stochastic matrices. The derivation of theorems is possible which are similar to
those derived for block-stochastic matrices by W. Kuich and K. Walk and for
quasi-stochastic matrices by Haynsworth. Among other theorems the theorem on the
group property, the reduction formula and its application to nonnegative
matrices holds in a modified manner. An example illustrates the definitions and
theorems.
