An introduction to semi-tensor product of matrices and its applications
Cheng, Daizhan.
An introduction to semi-tensor product of matrices and its applications [electronic resource] / Daizhan Cheng, Honsheng Qi, Yin Zhao. - Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2012. - 1 online resource (xxii, 587 pages) : illustrations
Includes bibliographical references (pages 573-581) and index.
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.
9814374687 9789814374682 9789814374699 9814374695
9786613906168
390616 MIL
Operator theory.
Matrices.
Spectral theory (Mathematics)
Matrices.
Operator theory.
Spectral theory (Mathematics)
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books.
Electronic books.
QA329 / .T74 2012eb
515.724
An introduction to semi-tensor product of matrices and its applications [electronic resource] / Daizhan Cheng, Honsheng Qi, Yin Zhao. - Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2012. - 1 online resource (xxii, 587 pages) : illustrations
Includes bibliographical references (pages 573-581) and index.
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.
9814374687 9789814374682 9789814374699 9814374695
9786613906168
390616 MIL
Operator theory.
Matrices.
Spectral theory (Mathematics)
Matrices.
Operator theory.
Spectral theory (Mathematics)
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books.
Electronic books.
QA329 / .T74 2012eb
515.724