Before revision:  Consequently, although the directand total requirement matrices are formulated and used for economic system analysis, the indirect requirements matrix has never been formulated before. Based on the system decomposition theory , the indirect transactions and the corresponding indirect requirements matrix are introduced in the present article for the first time.
After revision:  The novel concepts of the direct, indirect and total transactions between any two sectors are introduced, and the corresponding requirements matrices are systematically formulated relative to both final demands and gross outputs, based on the system decomposition theory , the indirect transactions and the corresponding indirect requirements matrix are introduced in the present article for the first time.