Before revision:  These existing formulations cannot quantify the indirect interactions  between any two sectors . The indirect transactions between two sectors of an economic system and the corresponding indirect requirements  are introduced in the present article , based on the system decomposition theory .
After revision:  These existing formulations cannot quantify the indirect interactions between any two sectors of an economic system. Therefore, although the direct and total requirement matrices are formulated and used for economic system analysis, the indirect requirements matrices has never been formulated before. Based on the system decomposition theory, the indirect transactions between two sectors of an economic system and the corresponding indirect requirements are introduced in the present article , based on the system decomposition theory .