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Linear Algebra Through Geometry
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Catalogue Information
Field name
Details
Dewey Class
512.5
Title
Linear Algebra Through Geometry ([EBook] /) / by Thomas Banchoff, John Wermer.
Author
Banchoff, Thomas
Added Personal Name
Wermer, John
author.
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : : Springer US, , 1983.
Physical Details
X, 257 p. : online resource.
Series
Undergraduate texts in mathematics
0172-6056
ISBN
9781468401615
Summary Note
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.:
Contents note
Preface -- Acknowledgments -- 1.0 Vectors in the Line -- 2.0 The Geometry of Vectors in the Plane -- 2.1 Transformations of the Plane -- 2.2 Linear Transformations and Matrices -- 2.3 Sums and Products of Linear Transformations -- 2.4 Inverses and Systems of Equations -- 2.5 Determinants -- 2.6 Eigenvalues -- 2.7 Classification of Conic Sections -- 2.8 Differential Systems -- 3.0 Vector Geometry in 3-Space -- 3.1 Transformations of 3-Space -- 3.2 Linear Transformations and Matrices -- 3.3 Sums and Products of Linear Transformations -- 3.4 Inverses and Systems of Equations -- 3.5 Determinants -- 3.6 Eigenvalues -- 3.7 Symmetric Matrices -- 3.8 Classification of Quadric Surfaces -- 4.0 Vector Geometry in 4-Space -- 4.1 Transformations of 4-Space -- 4.2 Linear Transformations and Matrices -- 5.1 Homogeneous Systems of Equations -- 5.2 Subspace, Linear Dependence, Dimension -- 5.3 Inhomogeneous Systems of Equations -- Afterword.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4684-0161-5
Links to Related Works
Subject References:
Algebra
.
Algebras, Linear
.
Geometry
.
Linear and Multilinear Algebras, Matrix Theory
.
Mathematics
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Matrix theory
.
Authors:
Banchoff, Thomas
.
Wermer, John
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Undergraduate texts in mathematics
.
Classification:
512.5
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