Abstract: This essay evaluates synthetically some coefficient matrices in analysis of input-output,and these matrices action in analysis of economic index,analysis of economic benefit and economy forecast.Investment coefficient matrix and approximate construction method are set forth.Optimal model in which profit is object function is advanced,and mathematical increment model is extended.A similar input-output coefficient matrix is created from a input-output coefficient matrix with matrix transformation method.

Key words: input-output coefficient matrix, investment coefficient matrix, price model, optimal model, analysis of conjunction, mathematical increment model