# Course in Linear Algebra

## Edition: N/A

### Authors: David B. Damiano, John B. Little

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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 Rn 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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