\u003cp\u003e\u003ci\u003eFrom Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems\u003c/i\u003e illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. \u003c/p\u003e\u003cul\u003e \u003cli\u003eProvides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems.\u003c/li\u003e \u003cli\u003eOffers potential applications to the analysis and control of new dimension-varying systems.\u003c/li\u003e \u003cli\u003eInvestigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.\u003c/li\u003e\u003c/ul\u003e
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