From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
- 1 Edición - 18 de mayo de 2019
- Última edición
- Autor: Daizhan Cheng
- Idioma: Inglés
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that exte… Leer más
Descripción
Descripción
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.
Puntos claves
Puntos claves
- Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems.
- Offers potential applications to the analysis and control of new dimension-varying systems.
- Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.
De interès para
De interès para
Upper-division undergraduates, graduate students, and researchers worldwide working in mathematics, economics, and engineering
Índice
Índice
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
Reseñas
Reseñas
Detalles del producto
Detalles del producto
- Edición: 1
- Última edición
- Publicado: 18 de mayo de 2019
- Idioma: Inglés
Sobre el autor
Sobre el autor
DC