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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)

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
Creator
Subject
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 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.--
Member of
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)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-98026-3
Instantiates
Publication
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
978-3-319-98026-3
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, non-commercial 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)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-98026-3
Publication
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
978-3-319-98026-3
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, non-commercial 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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