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The Fourier transform of the promotion is considered,which aims to develop a new model to solve complex data processing problems.This paper introduces the definition of multi-dimensional vector matrix.Based on the multidimensional vector matrix theory,the Fourier transformation is extended to multi-dimensional space,which includes the deduction of unitary orthogonal conjugate and energy concentration.Then the translation theory of twodimension Fourier transform is extended to multi-dimension space.