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MARC 21

Linear Algebra Through Geometry
Tag	Description
020	$a9781468401615$9978-1-4684-0161-5
082	$a512.5$223
099	$aOnline resource: Springer
100	$aBanchoff, Thomas.
245	$aLinear Algebra Through Geometry$h[EBook] /$cby Thomas Banchoff, John Wermer.
260	$aNew York, NY :$bSpringer US,$c1983.
300	$aX, 257 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aUndergraduate Texts in Mathematics,$x0172-6056
505	$aPreface -- 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.
520	$aIn 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aWermer, John.$eauthor.
710	$aSpringerLink (Online service)
830	$aUndergraduate Texts in Mathematics,$x0172-6056
856	$uhttp://dx.doi.org/10.1007/978-1-4684-0161-5