Boolean-valued matrices in the open Leontiev model

The article deals with boolean-valued matrices and the relations between such matrices and usual matrices with nonnegative elements. The main results are concerned with the canonical homomorphism between nonnegative matrices and boolean-valued matrices; this homomorphism allows to calculate the solution supports of linear equations with nonnegative matrices by the supports of right hand sides of these equations. Some applications to the open Leontiev models in mathematical economics are given.