In this paper，we discuss necessary and sufficient condition under which the one-dimensional general transforms equivalent to two-dimensional general transforms Theorem：Let [X]，[Y] be the matrix representations of vectors X，Y respectively，and let [R]，[Q]，[P] be three matrices of order N M x N M，N x N，M x M respectively，[X]，[Y] are of order N x M，X ，Y are dimension N M. (1) If and only if [R]=[P]^T [Q]，Y=[R]X and [Y]=[Q] [X] [Q] for any vector X，where denotes Kronecker Product of matrices; (2) If Y=[R]X and [Y]=[Q] [X] [P] for any vector X，then [R] is symmetric，if and only if [Q]，[P] are symmetric or anti-symmetric matrices，simultaneously，and R_i+jN,k+lN=±R_i+lN,k+jN R_i+jN,k+ln=±R_k+jN,i+lN (i，k=0，l，…，N-I;j,l=0，l，…，M-1) Nextly，we have discussed the equivalence of Walsh-Hadamard transforms and that of any general transforms having the cyclic convolution property (CCP)(DFT，NTT，PT). Lastly，we have introduced a fast algorithm of 2D-DFT-Vector Algorithm by using above equivalence theorem，which is more efficient than the row-column method of 2D-DFTs.