An introduction to semi-tensor product of matrices and its applications:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, N.J.
World Scientific
c2012
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| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Includes bibliographical references (p. 573-581) and index 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 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 |
| Physical Description: | 1 Online-Ressource (xxii, 587 p.) |
| ISBN: | 1283593718 9781283593717 9789814374682 9789814374699 9814374687 9814374695 |
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| 100 | 1 | |a Cheng, Dai-Zhan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to semi-tensor product of matrices and its applications |c Daizhan Cheng, Honsheng Qi, Yin Zhao |
| 264 | 1 | |a Hackensack, N.J. |b World Scientific |c c2012 | |
| 300 | |a 1 Online-Ressource (xxii, 587 p.) | ||
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| 500 | |a Includes bibliographical references (p. 573-581) and index | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 650 | 7 | |a MATHEMATICS / Functional Analysis |2 bisacsh | |
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| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 700 | 1 | |a Qi, Hongsheng |e Sonstige |4 oth | |
| 700 | 1 | |a Zhao, Yin |e Sonstige |4 oth | |
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| dewey-full | 515.724 |
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV043139748 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:40Z |
| institution | BVB |
| isbn | 1283593718 9781283593717 9789814374682 9789814374699 9814374687 9814374695 |
| language | English |
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| physical | 1 Online-Ressource (xxii, 587 p.) |
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| spelling | Cheng, Dai-Zhan Verfasser aut An introduction to semi-tensor product of matrices and its applications Daizhan Cheng, Honsheng Qi, Yin Zhao Hackensack, N.J. World Scientific c2012 1 Online-Ressource (xxii, 587 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 573-581) and index 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 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 MATHEMATICS / Functional Analysis bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast Operator theory Matrices Spectral theory (Mathematics) Qi, Hongsheng Sonstige oth Zhao, Yin Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=478628 Aggregator Volltext |
| spellingShingle | Cheng, Dai-Zhan An introduction to semi-tensor product of matrices and its applications MATHEMATICS / Functional Analysis bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast Operator theory Matrices Spectral theory (Mathematics) |
| 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 | an introduction to semi tensor product of matrices and its applications |
| topic | MATHEMATICS / Functional Analysis bisacsh Matrices fast Operator theory fast Spectral theory (Mathematics) fast Operator theory Matrices Spectral theory (Mathematics) |
| topic_facet | MATHEMATICS / Functional Analysis Matrices Operator theory Spectral theory (Mathematics) |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=478628 |
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