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A factorable Preisach distribution function is a reasonable assumption in modeling soft magnetic materials. With this assumption it is possible to define and employ a single-input Preisach function for easier implementation and identification of a scalar Preisach model. On the basis of this simplification, we developed a new method for identification and implementation of the isotropic vector Preisach model. With the aid of a newly derived equation, the Preisach function of the vector Preisach model can be identified from the corresponding scalar one. We verified the correctness of the proposed method by comparing the results of scalar and vector models in a scalar condition of input variation.