Linear Algebra Through Geometry
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Linear Algebra Through Geometry
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Author : Thomas Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-09-10
Linear Algebra Through Geometry written by Thomas Banchoff 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 1993-09-10 with Mathematics categories.
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.
Linear Algebra Through Geometry
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Author : T. Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra Through Geometry written by T. Banchoff 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 Mathematics categories.
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.
Linear Algebra Through Geometry
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Author : Thomas Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra Through Geometry written by Thomas Banchoff 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 Mathematics categories.
Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.
Linear Algebra With Geometric Applications
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Author : Larry E. Mansfield
language : en
Publisher:
Release Date : 1976
Linear Algebra With Geometric Applications written by Larry E. Mansfield and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Introduction To Linear And Matrix Algebra
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Author : Nathaniel Johnston
language : en
Publisher: Springer Nature
Release Date : 2021-05-19
Introduction To Linear And Matrix Algebra written by Nathaniel Johnston and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Mathematics categories.
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
Principles Of Linear Algebra With Mathematica
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Author : Kenneth M. Shiskowski
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-07
Principles Of Linear Algebra With Mathematica written by Kenneth M. Shiskowski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Mathematics categories.
A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings, and the commands required to solve complex and computationally challenging problems using Mathematica are provided. The book begins with an introduction to the commands and programming guidelines for working with Mathematica. Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, and vector projection are explored, as well as a unique variety of more advanced topics including rotations in space, 'rolling' a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, with an exploration of their effect on arclength, area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlessly integrated throughout the book through symbolic manipulations, numerical computations, graphics in two and three dimensions, animations, and programming. Each section concludes with standard problems in addition to problems that were specifically designed to be solved with Mathematica, allowing readers to test their comprehension of the presented material. All related Mathematica code is available on a corresponding website, along with solutions to problems and additional topical resources. Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Mathematica is an excellent book for courses on linear algebra at the undergraduate level. The book is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Mathematica to solve linear algebra problems.
Practical Linear Algebra
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Author : Gerald Farin
language : en
Publisher: CRC Press
Release Date : 2021-10-12
Practical Linear Algebra written by Gerald Farin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-12 with Mathematics categories.
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.
Linear Algebra Through Its Applications
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Author : Trevor James Fletcher
language : en
Publisher:
Release Date : 1972
Linear Algebra Through Its Applications written by Trevor James Fletcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Linear Algebra And Analytic Geometry
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Author : Bennie Marsh & Frankie Murray
language : en
Publisher: Scientific e-Resources
Release Date : 2018-01-18
Linear Algebra And Analytic Geometry written by Bennie Marsh & Frankie Murray and has been published by Scientific e-Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with categories.
In this book, the topics are presented in the same order as in the textbook. The problems concern two content areas: Linear Algebra, and Analytical Geometry. After reading this book, a student should be ables to solve linear equations and to perform the basic operations on numbers and algebraic expressions. The Linear Algebra tests will reveal readers' knowledge and skills, readers' abilities in interpreting symbols, justifying statements and constructing proofs. Readers should be able to apply the properties of determinants and matrix operations and solve linear systems of equations. The Analytical Geometry topics include different forms of equations of straight lines and planes; angles between simple figures; the curves of the second order. This book will prove definitive and ideal reference tool to research scholars, academicians and educationists.
Vectors Matrices And Geometry
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Author : K. T. Leung
language : en
Publisher: Kent State University Press
Release Date : 1994
Vectors Matrices And Geometry written by K. T. Leung and has been published by Kent State University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).