An introduction to semi-tensor product of matrices and its applications /:
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore ; Hackensack, NJ :
Distributed by World Scientific Pub.,
©2012.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xxii, 587 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 573-581) and index. |
| ISBN: | 9814374687 9789814374682 9789814374699 9814374695 1283593718 9781283593717 9786613906168 6613906166 |
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| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
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| 650 | 6 | |a Matrices. | |
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| 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. |
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| indexdate | 2024-11-27T13:24:56Z |
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| spelling | Cheng, Daizhan. An introduction to semi-tensor product of matrices and its applications / Daizhan Cheng, Honsheng Qi, Yin Zhao. Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2012. 1 online resource (xxii, 587 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 573-581) and index. Print version record. 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. 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. English. Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Théorie des opérateurs. Matrices. Spectre (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast Qi, Honsheng. Zhao, Yin. has work: An introduction to semi-tensor product of matrices and its applications (Text) https://id.oclc.org/worldcat/entity/E39PCGbpM73jrvD4FgRFTHtKr3 https://id.oclc.org/worldcat/ontology/hasWork Print version: 9786613906168 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=478628 Volltext |
| spellingShingle | Cheng, Daizhan An introduction to semi-tensor product of matrices and its applications / 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. Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Théorie des opérateurs. Matrices. Spectre (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85095029 http://id.loc.gov/authorities/subjects/sh85082210 http://id.loc.gov/authorities/subjects/sh85126408 |
| title | An introduction to semi-tensor product of matrices and its applications / |
| title_auth | An introduction to semi-tensor product of matrices and its applications / |
| title_exact_search | An introduction to semi-tensor product of matrices and its applications / |
| title_full | An introduction to semi-tensor product of matrices and its applications / Daizhan Cheng, Honsheng Qi, Yin Zhao. |
| title_fullStr | An introduction to semi-tensor product of matrices and its applications / Daizhan Cheng, Honsheng Qi, Yin Zhao. |
| title_full_unstemmed | An introduction to semi-tensor product of matrices and its applications / Daizhan Cheng, Honsheng Qi, Yin Zhao. |
| title_short | An introduction to semi-tensor product of matrices and its applications / |
| title_sort | introduction to semi tensor product of matrices and its applications |
| topic | Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Théorie des opérateurs. Matrices. Spectre (Mathématiques) MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast |
| topic_facet | Operator theory. Matrices. Spectral theory (Mathematics) Théorie des opérateurs. Spectre (Mathématiques) MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Matrices Operator theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=478628 |
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