From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems

From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product, a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. As dimension-varying systems are everywhere, this newly developed theory can revolutionize large data systems, such as genomics and bio-systems, deep learning, IT and information-based engineering applications.

• Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems
• Includes a brand new dimension-free matrix theory and cross-dimensional dynamic system theory
• Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid (semi-group with identity) of matrices with arbitrary dimensions