The Resource Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource)
Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource)
Resource Information
The item Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 "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 algebrageometric 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.
 Language
 eng
 Extent
 1 online resource (IX, 202 pages)
 Contents

 0. Introduction
 1. Scalar Linear Systems over the Complex Numbers
 2. Scalar Linear Systems over a Field k
 3. Factoring Polynomials
 4. Affine Algebraic Geometry: Algebraic Sets
 5. Affine Algebraic Geometry: The Hilbert Theorems
 6. Affine Algebraic Geometry: Irreducibility
 7. Affine Algebraic Geometry: Regular Functions and Morphisms I
 8. The Laurent Isomorphism Theorem
 9. Affine Algebraic Geometry: Regular Functions and Morphisms II
 10. The State Space: Realizations
 11. The State Space: Controllability, Observability, Equivalence
 12. Affine Algebraic Geometry: Products, Graphs and Projections
 13. Group Actions, Equivalence and Invariants
 14. The Geometric Quotient Theorem: Introduction
 15. The Geometric Quotient Theorem: Closed Orbits
 16. Affine Algebraic Geometry: Dimension
 17. The Geometric Quotient Theorem: Open on Invariant Sets
 18. Affine Algebraic Geometry: Fibers of Morphisms
 19. The Geometric Quotient Theorem: The Ring of Invariants
 20. Affine Algebraic Geometry: Simple Points
 21. Feedback and the Pole Placement Theorem
 22. Affine Algebraic Geometry: Varieties
 23. Interlude
 Appendix A: Tensor Products
 Appendix B: Actions of Reductive Groups
 Appendix C: Symmetric Functions and Symmetric Group Actions
 Appendix D: Derivations and Separability
 Problems
 References
 Isbn
 9783319980263
 Label
 Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry
 Title
 Methods of Algebraic Geometry in Control Theory: Part I
 Title remainder
 Scalar Linear Systems and Affine Algebraic Geometry
 Statement of responsibility
 by Peter Falb
 Language
 eng
 Summary
 "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 algebrageometric 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.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Falb, Peter
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Modern Birkhäuser Classics,
 Springer eBooks
 Springer eBooks.
 http://library.link/vocab/subjectName
 Geometry, algebraic
 Label
 Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 0. Introduction  1. Scalar Linear Systems over the Complex Numbers  2. Scalar Linear Systems over a Field k  3. Factoring Polynomials  4. Affine Algebraic Geometry: Algebraic Sets  5. Affine Algebraic Geometry: The Hilbert Theorems  6. Affine Algebraic Geometry: Irreducibility  7. Affine Algebraic Geometry: Regular Functions and Morphisms I  8. The Laurent Isomorphism Theorem  9. Affine Algebraic Geometry: Regular Functions and Morphisms II  10. The State Space: Realizations  11. The State Space: Controllability, Observability, Equivalence  12. Affine Algebraic Geometry: Products, Graphs and Projections  13. Group Actions, Equivalence and Invariants  14. The Geometric Quotient Theorem: Introduction  15. The Geometric Quotient Theorem: Closed Orbits  16. Affine Algebraic Geometry: Dimension  17. The Geometric Quotient Theorem: Open on Invariant Sets  18. Affine Algebraic Geometry: Fibers of Morphisms  19. The Geometric Quotient Theorem: The Ring of Invariants  20. Affine Algebraic Geometry: Simple Points  21. Feedback and the Pole Placement Theorem  22. Affine Algebraic Geometry: Varieties  23. Interlude  Appendix A: Tensor Products  Appendix B: Actions of Reductive Groups  Appendix C: Symmetric Functions and Symmetric Group Actions  Appendix D: Derivations and Separability  Problems  References
 Control code
 9783319980263
 Dimensions
 unknown
 Extent
 1 online resource (IX, 202 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319980263
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 3 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1055594210
 Label
 Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 0. Introduction  1. Scalar Linear Systems over the Complex Numbers  2. Scalar Linear Systems over a Field k  3. Factoring Polynomials  4. Affine Algebraic Geometry: Algebraic Sets  5. Affine Algebraic Geometry: The Hilbert Theorems  6. Affine Algebraic Geometry: Irreducibility  7. Affine Algebraic Geometry: Regular Functions and Morphisms I  8. The Laurent Isomorphism Theorem  9. Affine Algebraic Geometry: Regular Functions and Morphisms II  10. The State Space: Realizations  11. The State Space: Controllability, Observability, Equivalence  12. Affine Algebraic Geometry: Products, Graphs and Projections  13. Group Actions, Equivalence and Invariants  14. The Geometric Quotient Theorem: Introduction  15. The Geometric Quotient Theorem: Closed Orbits  16. Affine Algebraic Geometry: Dimension  17. The Geometric Quotient Theorem: Open on Invariant Sets  18. Affine Algebraic Geometry: Fibers of Morphisms  19. The Geometric Quotient Theorem: The Ring of Invariants  20. Affine Algebraic Geometry: Simple Points  21. Feedback and the Pole Placement Theorem  22. Affine Algebraic Geometry: Varieties  23. Interlude  Appendix A: Tensor Products  Appendix B: Actions of Reductive Groups  Appendix C: Symmetric Functions and Symmetric Group Actions  Appendix D: Derivations and Separability  Problems  References
 Control code
 9783319980263
 Dimensions
 unknown
 Extent
 1 online resource (IX, 202 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319980263
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 3 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1055594210
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/MethodsofAlgebraicGeometryinControlTheory/ZiaW5624UWI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/MethodsofAlgebraicGeometryinControlTheory/ZiaW5624UWI/">Methods of Algebraic Geometry in Control Theory: Part I : Scalar Linear Systems and Affine Algebraic Geometry, by Peter Falb, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>