Course in Linear Algebra

ISBN-10: 0486469085

ISBN-13: 9780486469089

Edition: N/A

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Description:

Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction, definitions, and propositions, in addition to multiple examples, lemmas, theorems, corollaries, and proofs. Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end. 1988 edition.
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Book details

List price: $26.95
Publisher: Dover Publications, Incorporated
Publication date: 9/14/2011
Binding: Paperback
Pages: 464
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.672
Language: English

Preface
Errata
A Guide to the Exercises
Vector Spaces
Introduction
Vector Spaces
Subspaces
Linear Combinations
Linear Dependence and Linear Independence
Interlude on Solving Systems of Linear Equations
Bases and Dimension
Chapter Summary
Supplementary Exercises
Linear Transformations
Introduction
Linear Transformations
Linear Transformations between Finite-Dimensional Spaces
Kernel and Image
Applications of the Dimension Theorem
Composition of Linear Transformations
The Inverse of a Linear Transformation
Change of Basis
Chapter Summary
Supplementary Exercises
The Determinant Function
Introduction
The Determinant as Area
The Determinant of an n x n Matrix
Further Properties of the Determinant
Chapter Summary
Supplementary Exercises
Eigenvalues, Eigenvectors, Diagonalization, and the Spectral Theorem in R<sup>n</sup>
Introduction
Eigenvalues and Eigenvectors
Diagonalizability
Geometry in Rn
Orthogonal Projections and the Gram-Schmidt Process
Symmetric Matrices
The Spectral Theorem
Chapter Summary
Supplementary Exercises
Complex; Numbers and Complex Vector Spaces
Introduction
Complex Numbers
Vector Spaces Over a Field
Geometry in a Complex Vector Space
Chapter Summary
Supplementary Exercises
Jordan Canonical Form
Introduction
Triangular Form
A Canonical Form for Nilpotent Mappings
Jordan Canonical Form
Computing Jordan Form
The Characteristic Polynomial and the Minimal Polynomial
Chapter Summary
Supplementary Exercises
Differential Equations
Introduction
Two Motivating Examples
Constant Coefficient Linear Differential Equations The Diagonalizable Case
Constant (Coefficient Linear Differential Equations: The General Case
One Ordinary Differential Equation with Constant Coefficients
An Eigenvalue Problem
Chapter Summary
Supplementary Exercises
Some Basic Logic and Set Theory
Sets
Statements and Logical Operators
Statements with Quantifiers
Further Notions from Set Theory
Relations and Functions
Injectivity, Surjectivity, and Bijectivity
Composites and Inverse Mappings
Some (Optional) Remarks on Mathematics and Logic
Mathematical Induction
Solutions
Index
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