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Statistical independence of multivariate contingency tables

This paper focuses on statistical independence of multiple variables from the viewpoint of linear algebra. While information granules of statistical independence of two variables can be viewed as determinants of 2 × 2- submatrices, those of three variables consist of several combination s of determinants. However, this combination can be viewed as a linear sum over the all combinarial pairs of 2×2 -matrix, where 2×2 matrix form can be viewed as a fundamental granule for statistical independence.