Linear Algebra Through Geometry

Linear Algebra Through Geometry by Thomas Banchoff, John Wermer.

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 direc...

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Bibliographic Details
Main Authors: Banchoff, Thomas (Author), Wermer, John (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1992.
Edition:2nd ed. 1992.
Series:Undergraduate Texts in Mathematics,
Springer eBook Collection.
Subjects:
Matrix theory.
Algebra.
Geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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
  • 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 n-Space, n ? 4
  • 4.1 Transformations of n-Space, n ? 4
  • 4.2 Linear Transformations and Matrices
  • 4.3 Homogeneous Systems of Equations in n-Space
  • 4.4 Inhomogeneous Systems of Equations in n-Space
  • 5.0 Vector Spaces
  • 5.1 Bases and Dimensions
  • 5.2 Existence and Uniqueness of Solutions
  • 5.3 The Matrix Relative to a Given Basis
  • 6.0 Vector Spaces with an Inner Product
  • 6.1 Orthonormal Bases
  • 6.2 Orthogonal Decomposition of a Vector Space
  • 7.0 Symmetric Matrices in n Dimensions
  • 7.1 Quadratic Forms in n Variables
  • 8.0 Differential Systems
  • 8.1 Least Squares Approximation
  • 8.2 Curvature of Function Graphs.

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