Port Area Distribution and Marine Economic Prediction Based on Kronecker Direct-Product of the Meet-Matrix

Meet-matrices are widely used in the age of big data & information. This paper has conducted a study on the gcd-matrix over Descartes direct product of some finite partial-order sets. The structure and bounds of the determinant of direct product of gcd- matrix (GCD matrix) are searched because of Mobius inversion method and tensor product theory. On the finite natural number set, we have got some results of the direct product of the meet matrix similar to the gcd-matrix on the poset. Finally, according to the results the author and collaborator have already generalized the good-looking outcome to get the determinant of the Kronecker direct-product meet matrix on the general partial order set.