| Description |
1 online resource (xxii, 587 pages) : illustrations |
| 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 |
| Bibliography |
Includes bibliographical references (pages 573-581) and index |
| Notes |
English |
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Print version record |
| Subject |
Operator theory.
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Matrices.
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Spectral theory (Mathematics)
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Matrices
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Operator theory
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Spectral theory (Mathematics)
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| Form |
Electronic book
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| Author |
Qi, Honsheng
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Zhao, Yin
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| ISBN |
9814374687 |
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9789814374682 |
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9789814374699 |
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9814374695 |
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1283593718 |
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9781283593717 |
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9786613906168 |
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6613906166 |
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