Parsing Economic Technology Matrices by Triangular Decomposition

An input–output technology with intermediate inputs is said to be productive or viable if it allows for positive net amounts of every commodity. Each division or sector will then contribute less than one unit of direct and indirect intermediate inputs to the making of one unit of its own output. Equivalently, the leading principal minors of the technology’s associated Leontief matrix are all positive (Hawkins–Simon condition). We demonstrate that the minors can be checked efficiently in the course of a triangular decomposition of this matrix. Copyright Springer Science + Business Media, Inc. 2005