Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness,
and overall student usability. Its inclusion of calculus-related examples, true/false problems, section summaries,
integrated applications, and coverage of Cn make it a superb text for the sophomore or junior-level linear algebra
course. This Third Edition retains the features that have made it successful over the years, while addressing recent
developments of how linear algebra is taught and learned. Key concepts are presented early on, with an emphasis
on geometry. The text features earlier presentation of definitions, proofs, and theorems previously introduced
only in the abstract, a more concise vector space chapter, new applications, and optional integration of MATLAB
and LINTEK through specially labeled computer exercises. In addition, LINTEK, the exploratory software package
developed exclusively for this text, has been thoroughly revised so as to be faster, more user-friendly, and more
functional.
Table of Contents
Chapter 1: Vectors, Matrices, and Linear Systems
Vectors in Euclidean Spaces
The Norm and the Dot Product
Matrices and Their Algebra
Solving Systems of Linear Equations
Inverses of Square Matrices
Homogeneous Systems, Subspaces, and Bases
Application to Population Distribution (Optional)
Application to Binary Linear Codes (Optional)
Chapter 2: Dimension, Rank, and Linear Transformations
Independence and Dimension
The Rank of a Matrix
Linear Transformations of Euclidean Spaces
Linear Transformations of the Plane (Optional)
Lines, Planes, and Other Flats (Optional)
Chapter 3: Vector Spaces
Vector Spaces
Basic Concepts of Vector Spaces
Coordinatization of Vectors
Linear Transformations
Inner-Product Spaces (Optional)
Chapter 4: Determinants
Areas, Volumes, and Cross Products
The Determinant of a Square Matrix
Computation of Determinants and Cramer's Rule
Linear Transformations and Determinants (Optional)
Chapter 5: Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Diagonalization
Two Applications
Chapter 6: Orthogonality
Projections
The Gram-Schmidt Process
Orthogonal Matrices
The Projection Matrix
The Method of Least Squares
Chapter 7: Change of Basis
Coordinatization and Change of Basis
Matrix Representations and Similarity
Chapter 8: Eigenvalues: Further Applications and Computations
Diagonalization of Quadratic Forms
Applications to Geometry
Applications to Extrema
Computing Eigenvalues and Eigenvectors
Chapter 9: Complex Scalars
Algebra of Complex Numbers
Matrices and Vector Spaces with Complex Scalars
Eigenvalues and Diagonalization
Jordan Canonical Form
Chapter 10: Solving Large Linear Systems
Considerations of Time
The LU-Factorization
Pivoting, Scaling, and Ill-Conditioned Matrices
Appendices
Mathematical Induction
Two Deferred Proofs
LINTEK Routines
MATLAB Procedures and Commands Used in the Exercises
