Author | Banchoff, Thomas. author |
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Title | Linear Algebra Through Geometry [electronic resource] / by Thomas Banchoff, John Wermer |
Imprint | New York, NY : Springer US, 1992 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4390-8 |
Descript | XII, 308 p. online resource |
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