Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)

Banchoff, Thomas

ISBN 10: 0387975861 / ISBN 13: 9780387975863

Editore: Springer, 1991

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Dati bibliografici

• Titolo: Linear Algebra Through Geometry (Undergraduate Texts in Mathematics)
• Editore: Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 0387975861
• ISBN 13: 9780387975863
• Rilegatura: Rilegato
• Edizione: seconda edizione
• Condizione: Very Good

Descrizione articolo

Riassunto

Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces.

Contenuti

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.