| Description |
1 online resource (xxii, 587 pages) : illustrations |
|
text file |
| Bibliography |
Includes bibliographical references (pages 573-581) and index. |
| Contents |
Multi-dimensional data -- Semi-tensor product of matrices -- Multilinear mappings among vector spaces -- Right and general semi-tensor products -- Rank, pseudo-inverse, and positivity of STP -- Matrix expression of logic -- Mix-valued logic -- Logical matrix, fuzzy set and fuzzy logic -- Fuzzy relational equation -- Fuzzy control with coupled fuzzy relations -- Representation of boolean functions -- Decomposition of logical functions -- Boolean calculus -- Lattice, graph, and universal algebra -- Boolean network -- Boolean control system -- Game theory -- Multi-variable polynomials -- Some applications to differential geometry and algebra -- Morgan's problem -- Linearization of nonlinear control systems -- Stability region of dynamic systems. |
| Summary |
A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations. This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Operator theory.
|
|
Operator theory. |
|
Matrices.
|
|
Matrices. |
|
Spectral theory (Mathematics)
|
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Spectral theory (Mathematics) |
| Genre/Form |
Electronic books.
|
|
Electronic books.
|
| Added Author |
Qi, Honsheng.
|
|
Zhao, Yin.
|
| Other Form: |
Print version: 9786613906168 |
| ISBN |
9814374687 (cloth) |
|
9789814374682 (cloth) |
|
9789814374699 |
|
9814374695 |
|
1283593718 |
|
9781283593717 |
| Standard No. |
9786613906168 |
|
