From dimension-free matrix theory to cross-dimensional dynamic systems
著者
書誌事項
From dimension-free matrix theory to cross-dimensional dynamic systems
（Mathematics in science and engineering : a series of monographs and textbooks）
Academic Press, c2019
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems 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.
目次
1. Semi-tensor product of matrices2. Boolean networks3. Finite games4. Equivalence and lattice structures5. Topological structure on quotient space6. Differential geometry on set of matrices7. Cross-dimensional Lie algebra and Lie group8. Second matrix-matrix semi-tensor product9. Structure on set of vectors10. Dimension-varying linear system11. Dimension-varying linear control system12. Generalized dynamic systems13. Dimension-varying nonlinear dynamic systemsA. Mathematical preliminaries
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