Linear Systems Theory Introductory Algebraic Geometry
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Linear Systems Theory Introductory Algebraic Geometry
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Author : Róbert Hermann
language : en
Publisher: Math-Sci Press
Release Date : 1974
Linear Systems Theory Introductory Algebraic Geometry written by Róbert Hermann and has been published by Math-Sci Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Methods Of Algebraic Geometry In Control Theory Part I
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Author : Peter Falb
language : en
Publisher: Springer
Release Date : 2018-08-25
Methods Of Algebraic Geometry In Control Theory Part I written by Peter Falb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-25 with Mathematics categories.
"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik
Methods Of Algebraic Geometry In Control Theory Part Ii
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Author : Peter Falb
language : en
Publisher: Springer
Release Date : 2018-09-14
Methods Of Algebraic Geometry In Control Theory Part Ii written by Peter Falb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-14 with Science categories.
"An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebra-geometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler single-input–single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews
Introduction To Algebraic Geometry
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Author : Serge Lang
language : en
Publisher: Courier Dover Publications
Release Date : 2019-03-20
Introduction To Algebraic Geometry written by Serge Lang and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Geometrical Methods For The Theory Of Linear Systems
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Author : C.I. Byrnes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometrical Methods For The Theory Of Linear Systems written by C.I. Byrnes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The lectures contained in this book were presented at Harvard University in June 1979. The workshop at which they were presented was the third such on algebro-geometric methods. The first was held in 1973 in London and the emphasis was largely on geometric methods. The second was held at Ames Research Center-NASA in 1976. There again the emphasis was on geometric methods, but algebraic geometry was becoming a dominant theme. In the two years after the Ames meeting there was tremendous growth in the applications of algebraic geometry to systems theory and it was becoming clear that much of the algebraic systems theory was very closely related to the geometric systems theory. On this basis we felt that this was the right time to devote a workshop to the applications of algebra and algebraic geometry to linear systems theory. The lectures contained in this volume represent all but one of the tutorial lectures presented at the workshop. The lec ture of Professor Murray Wonham is not contained in this volume and we refer the interested to the archival literature. This workshop was jointly sponsored by a grant from Ames Research Center-NASA and a grant from the Advanced Study Institute Program of NATO. We greatly appreciate the financial support rendered by these two organizations. The American Mathematical Society hosted this meeting as part of their Summer Seminars in Applied Mathematics and will publish the companion volume of con tributed papers.
Introduction To Algebraic Geometry
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Author : Steven Dale Cutkosky
language : en
Publisher:
Release Date : 2018
Introduction To Algebraic Geometry written by Steven Dale Cutkosky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry, Algebraic categories.
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic 0 and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More.
Max Linear Systems Theory And Algorithms
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Author : Peter Butkovič
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Max Linear Systems Theory And Algorithms written by Peter Butkovič and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-05 with Mathematics categories.
Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.
Algebraic And Geometric Methods In Linear Systems Theory
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Author : Christopher I. Byrnes
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Algebraic And Geometric Methods In Linear Systems Theory written by Christopher I. Byrnes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Max Linear Systems
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Author : Peter Butkovi
language : en
Publisher:
Release Date : 2010-09-13
Max Linear Systems written by Peter Butkovi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-13 with categories.
Algebro Geometric And Lie Theoretic Techniques In Systems Theory
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Author : Robert Hermann
language : en
Publisher:
Release Date : 1977
Algebro Geometric And Lie Theoretic Techniques In Systems Theory written by Robert Hermann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Continuous groups categories.