Statistical independence of three variables and contingency matrix

This paper focuses on statistical independence of three variables from the viewpoint of linear algebra. While information granules of statistical independence of two variables can be viewed as determinants of 2 x 2- submatrices, those of three variables consist of several combinations of determinants. Thus, even in the case of three attributes, 2 x 2 submatrices play an important role in measuring the degree of statistical independence.