Practical Linear Algebra: A Geometry Toolbox
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- Type：Epub+TxT+PDF+Mobi
- Create Date：2021-11-08 16:16:04
- Update Date：2025-09-23
- Status：finish
- Author：Gerald Farin
- ISBN：0367507846
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Summary
Linear algebra is growing in importance。 3D entertainment， animations in movies and video games are developed using linear algebra。 Animated characters are generated using equations straight out of this book。 Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology。
The Fourth Edition of this popular text introduces linear algebra in a comprehensive， geometric， and algorithmic way。 The authors start with the fundamentals in 2D and 3D， then move on to higher dimensions， expanding on the fundamentals and introducing new topics， which are necessary for many real-life applications and the development of abstract thought。 Applications are introduced to motivate topics。
The subtitle， A Geometry Toolbox， hints at the book's geometric approach， which is supported by many sketches and figures。 Furthermore， the book covers applications of triangles， polygons， conics， and curves。 Examples demonstrate each topic in action。
This practical approach to a linear algebra course， whether through classroom instruction or self-study， is unique to this book。
New to the Fourth Edition:
Ten new application sections。 A new section on change of basis。 This concept now appears in several places。 Chapters 14-16 on higher dimensions are notably revised。 A deeper look at polynomials in the gallery of spaces。 Introduces the QR decomposition and its relevance to least squares。 Similarity and diagonalization are given more attention as are eigenfunctions。 A longer thread on least squares， running from orthogonal projections to a solution via SVD and the pseudoinverse。 More applications for PCA have been added。 More examples， exercises， and more on the kernel and general linear spaces。 A list of applications has been added in Appendix A。 The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics， engineering， science， computer graphics， and geometric modeling。
Table of Contents
Preface
Descartes' Discovery Here and There: Points and Vectors in 2D Lining Up: 2D Lines Changing Shapes: Linear Maps in 2D 2 � 2 Linear Systems Moving Things Around: Affine Maps in 2D Eigen Things 3D Geometry Linear Maps in 3D Affine Maps in 3D Interactions in 3D Gauss or Linear Systems Alternative System Solvers General Linear Spaces Eigen Things Revisited The Singular Value Decomposition Breaking It Up: Triangles Putting Lines Together: Polylines and Polygons Conics Curves Appendices
Applications
Glossary
Select Exercise Solutions Bibliography
Biography
Gerald Farin （deceased） was a professor in the School of Computing， Informatics， and Design Systems Engineering （CIDSE） at Arizona State University。 He received his doctoral degree in mathematics from the University of Braunschweig， Germany。 His extensive experience in geometric design started at Daimler-Benz。 He was a founding member of the editorial board for the journal Computer-Aided Geometric Design （Elsevier）， and he served as co-editor in chief for more than 20 years。 He published more than 100 research papers。 Gerald also organized numerous conferences and authored or edited 29 books。 This includes his much read and referenced textbook Curves and Surfaces for CAGD and his book on NURBS。 In addition to this book， Gerald and Dianne co-authored The Essentials of CAGD， Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press。
Dianne Hansford， received her Ph。D。 from Arizona State University。 Her research interests are in the field of geometric modeling with a focus on industrial curve and surface applications related to mathematical definitions of shape。 Together with Gerald Farin （deceased）， she delivered custom software solutions， advisement on best practices， and taught on-site courses as a consultant。 She is a co-founder of 3D Compression Technologies。 She is now lecturer in the School of Computing， Informatics， and Design Systems Engineering （CIDSE） at Arizona State University， primarily teaching geometric design， computer graphics， and scientific computing and visualization。 In addition to this book， Gerald and Dianne co-authored The Essentials of CAGD， Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press。
The Fourth Edition of this popular text introduces linear algebra in a comprehensive， geometric， and algorithmic way。 The authors start with the fundamentals in 2D and 3D， then move on to higher dimensions， expanding on the fundamentals and introducing new topics， which are necessary for many real-life applications and the development of abstract thought。 Applications are introduced to motivate topics。
The subtitle， A Geometry Toolbox， hints at the book's geometric approach， which is supported by many sketches and figures。 Furthermore， the book covers applications of triangles， polygons， conics， and curves。 Examples demonstrate each topic in action。
This practical approach to a linear algebra course， whether through classroom instruction or self-study， is unique to this book。
New to the Fourth Edition:
Ten new application sections。 A new section on change of basis。 This concept now appears in several places。 Chapters 14-16 on higher dimensions are notably revised。 A deeper look at polynomials in the gallery of spaces。 Introduces the QR decomposition and its relevance to least squares。 Similarity and diagonalization are given more attention as are eigenfunctions。 A longer thread on least squares， running from orthogonal projections to a solution via SVD and the pseudoinverse。 More applications for PCA have been added。 More examples， exercises， and more on the kernel and general linear spaces。 A list of applications has been added in Appendix A。 The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics， engineering， science， computer graphics， and geometric modeling。
Table of Contents
Preface
Descartes' Discovery Here and There: Points and Vectors in 2D Lining Up: 2D Lines Changing Shapes: Linear Maps in 2D 2 � 2 Linear Systems Moving Things Around: Affine Maps in 2D Eigen Things 3D Geometry Linear Maps in 3D Affine Maps in 3D Interactions in 3D Gauss or Linear Systems Alternative System Solvers General Linear Spaces Eigen Things Revisited The Singular Value Decomposition Breaking It Up: Triangles Putting Lines Together: Polylines and Polygons Conics Curves Appendices
Applications
Glossary
Select Exercise Solutions Bibliography
Biography
Gerald Farin （deceased） was a professor in the School of Computing， Informatics， and Design Systems Engineering （CIDSE） at Arizona State University。 He received his doctoral degree in mathematics from the University of Braunschweig， Germany。 His extensive experience in geometric design started at Daimler-Benz。 He was a founding member of the editorial board for the journal Computer-Aided Geometric Design （Elsevier）， and he served as co-editor in chief for more than 20 years。 He published more than 100 research papers。 Gerald also organized numerous conferences and authored or edited 29 books。 This includes his much read and referenced textbook Curves and Surfaces for CAGD and his book on NURBS。 In addition to this book， Gerald and Dianne co-authored The Essentials of CAGD， Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press。
Dianne Hansford， received her Ph。D。 from Arizona State University。 Her research interests are in the field of geometric modeling with a focus on industrial curve and surface applications related to mathematical definitions of shape。 Together with Gerald Farin （deceased）， she delivered custom software solutions， advisement on best practices， and taught on-site courses as a consultant。 She is a co-founder of 3D Compression Technologies。 She is now lecturer in the School of Computing， Informatics， and Design Systems Engineering （CIDSE） at Arizona State University， primarily teaching geometric design， computer graphics， and scientific computing and visualization。 In addition to this book， Gerald and Dianne co-authored The Essentials of CAGD， Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press。
Reviews
Farsan Rashid
，
The first time I learned about geometric interpretation of Linear Algebra was from famous Youtube channel 3blue1brown， it was opening of a new horizon。 After that I decided to read a book to be 'formally' introduced with major concepts in LA and learn about topics that are frequently mentioned in Machine learning （eigen， SVD， PCA etc）。 I tried Gilbert Strang but found it too dry so decided to find books that describes LA in the light of geometry and also covers all the keywords I had in mind。 Th The first time I learned about geometric interpretation of Linear Algebra was from famous Youtube channel 3blue1brown， it was opening of a new horizon。 After that I decided to read a book to be 'formally' introduced with major concepts in LA and learn about topics that are frequently mentioned in Machine learning （eigen， SVD， PCA etc）。 I tried Gilbert Strang but found it too dry so decided to find books that describes LA in the light of geometry and also covers all the keywords I had in mind。 This book fitted in every aspect。 I don't know whether I would have equally enjoyed or so easily grasped the concepts if I had not watched the 3blue1brown videos but also I do not find a single scope where the author could have done better。 Every single topic （vector， matrix， inverse， shear， rotation， eigen， Gram-Schmidt， SVD， PCA etc。。。） is wonderfully explained both in 2D and 3D setting， also some dedicated chapters to discuss about higher dimensions。 The book website （http://www。farinhansford。com/books/pl。。。） contains lecture slides， images used in the book， Mathemetica scripts（to generate image）， solution to exercises （for instructors）。 I suggest to take a look at the book if someone is teaching undergraduate LA。The book also has lots of real life examples， almost all of them are related to graphics but also has some interesting examples like Google page rank matrix。IMO title of this book is misleading and should have been something like "Geometric Interpretation of Linear Algebra"。My respect to the departed soul of author Gerald Farin who passed away on 14 January 2016 for this amazing book。 。。。more
Hilary Chang
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This book uses a lot of pictures to show you how linear algebra applies in geometry and explains it in plain language。 I'm never a fan of mathematics; but I find reading it enjoyable。 I highly recommend this book to anyone who has done linear algebra but doesn't know what's the point of learning it， or who just wants to have some puzzles after a busy day。 This book uses a lot of pictures to show you how linear algebra applies in geometry and explains it in plain language。 I'm never a fan of mathematics; but I find reading it enjoyable。 I highly recommend this book to anyone who has done linear algebra but doesn't know what's the point of learning it， or who just wants to have some puzzles after a busy day。 。。。more
Jia Chen
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Wonderful book for people who study computer graphics。
Charles
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Linear algebra has traditionally been the class in the undergraduate math curriculum where the student makes the transition from "plug - n - chug" formula popping to mathematical proofs。 However， in recent years linear algebra has taken on a new role， namely as the best class where applied mathematics can be visually demonstrated。 The enormous advances in animated imagery have led to movies where the characters are a virtual hybrid of animated and real。 I once taught a course in computer graphic Linear algebra has traditionally been the class in the undergraduate math curriculum where the student makes the transition from "plug - n - chug" formula popping to mathematical proofs。 However， in recent years linear algebra has taken on a new role， namely as the best class where applied mathematics can be visually demonstrated。 The enormous advances in animated imagery have led to movies where the characters are a virtual hybrid of animated and real。 I once taught a course in computer graphics for computer programmers and they were impressed when they applied a basic matrix multiplication to a figure and could watch the altered figure appear on the screen， albeit slowly。 Quite frankly， they loved the course。This book covers linear algebra before the appearance of formal proofs; I cannot recall seeing a single proof。 That coverage is excellent and is focused on how images are created and modified using linear algebra。 It is clearly written and illustrated and a tutorial on PostScript appears in an appendix。 There is a set of exercises at the end of each chapter and the solutions to many of them are included。A textbook for the modern use of linear algebra as an image creation and modification tool， it is ideal for any math program that wants to cover that material。 In my experience， it would be a very popular course， but it cannot be used for any coverage of linear algebra that involves proofs。Published in Journal of Recreational Mathematics， reprinted with permission and this review appears on Amazon 。。。more
Bengt
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