ISBN-10:
1482299283
ISBN-13:
2901482299280
Pub. Date:
12/02/2014
Publisher:
Taylor & Francis
Linear Algebra, Geometry and Transformation / Edition 1

Linear Algebra, Geometry and Transformation / Edition 1

by Bruce Solomon
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Product Details

ISBN-13: 2901482299280
Publisher: Taylor & Francis
Publication date: 12/02/2014
Series: Textbooks in Mathematics Series
Edition description: New Edition
Pages: 474
Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

About the Author

Bruce Solomon is a professor in the Department of Mathematics at Indiana University Bloomington, where he often teaches linear algebra. He has held visiting positions at Stanford University and in Australia, France, and Israel. His research articles explore differential geometry and geometric variational problems. He earned a PhD from Princeton University.

Table of Contents

Vectors, Mappings and Linearity
Numeric Vectors
Functions
Mappings and Transformations
Linearity
The Matrix of a Linear Transformation

Solving Linear Systems
The Linear System
The Augmented Matrix and RRE Form
Homogeneous Systems in RRE Form
Inhomogeneous Systems in RRE Form
The Gauss-Jordan Algorithm
Two Mapping Answers

Linear Geometry
Geometric Vectors
Geometric/Numeric Duality
Dot-Product Geometry
Lines, Planes, and Hyperplanes
System Geometry and Row/Column Duality

The Algebra of Matrices
Matrix Operations
Special Matrices
Matrix Inversion
A Logical Digression
The Logic of the Inversion Algorithm
Determinants

Subspaces
Basic Examples and Definitions
Spans and Perps
Nullspace
Column-Space
Perp/Span Conversion
Independence
Basis
Dimension and Rank

Orthogonality
Orthocomplements
Four Subspaces, 16 Questions
Orthonormal Bases
The Gram-Schmidt Algorithm

Linear Transformation
Kernel and Image
The Linear Rank Theorem
Eigenspaces
Eigenvalues and Eigenspaces: Calculation
Eigenvalues and Eigenspaces: Similarity
Diagonalizability and the Spectral Theorem
Singular Value Decomposition

Appendix A: Determinants
Appendix B: Proof of the Spectral Theorem
Appendix C: Lexicon

Index

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