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Linear Algebra Through Geometry

Linear Algebra Through Geometry
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.
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