Linear Algebra

ISBN-10: 0130084514
ISBN-13: 9780130084514
Edition: 4th 2003
List price: $209.80 Buy it from $13.44 Rent it from $47.45
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Description: This bestselling theorem-proof text presents a careful treatment of the principal topics of linear algebra, illustrating the power of the subject through a variety of applications.

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Book details

List price: $209.80
Edition: 4th
Copyright year: 2003
Publisher: Prentice Hall PTR
Publication date: 11/11/2002
Binding: Hardcover
Pages: 601
Size: 6.00" wide x 9.25" long x 1.25" tall
Weight: 2.112

This bestselling theorem-proof text presents a careful treatment of the principal topics of linear algebra, illustrating the power of the subject through a variety of applications.

Vector Spaces.
Introduction
Vector Spaces
Subspaces
Linear Combinations and Systems of Linear Equations
Linear Dependence and Linear Independence
Bases and Dimension
Maximal Linearly Independent Subsets
Linear Transformations and Matrices
Linear Transformations, Null Spaces, and Ranges
The Matrix Representation of a Linear Transformation
Composition of Linear Transformations and Matrix Multiplication
Invertibility and Isomorphisms
The Change of Coordinate Matrix
Dual Spaces
Homogeneous Linear Differential Equations with Constant Coefficients
Elementary Matrix Operations and Systems of Linear Equations
Elementary Matrix Operations and Elementary Matrices
The Rank of a Matrix and Matrix Inverses
Systems of Linear EquationsTheoretical Aspects
Systems of Linear EquationsComputational Aspects
Determinants
Determinants of Order 2
Determinants of Order n
Properties of Determinants
SummaryImportant Facts about Determinants
A Characterization of the Determinant
Diagonalization
Eigenvalues and Eigenvectors
Diagonalizability
Matrix Limits and Markov Chains
Invariant Subspaces and the Cayley-Hamilton Theorem
Inner Product Spaces
Inner Products and Norms
The Gram-Schmidt Orthogonalization Process and Orthogonal Complements
The Adjoint of a Linear Operator
Normal and Self-Adjoint Operators
Unitary and Orthogonal Operators and Their Matrices
Orthogonal Projections and the Spectral Theorem
The Singular Value Decomposition and the Pseudoinverse
Bilinear and Quadratic Forms
Einstein's Special Theory of Relativity
Conditioning and the Rayleigh Quotient
The Geometry of Orthogonal Operators
Canonical Forms
The Jordan Canonical Form I
The Jordan Canonical Form II
The Minimal Polynomial
Rational Canonical Form
Appendices
Sets
Functions
Fields
Complex Numbers
Polynomials
Answers to Selected Exercises
Index

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