Linear Algebra

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  • Edition: 3rd
  • Format: Paperback
  • Copyright: 1994-12-31
  • Publisher: Pearson

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Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness, and overall 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. KEY TOPICS:Vectors, Matrices, and Linear Systems; Dimension, Rank, and Linear Transformations; Vector Spaces; Determinants; Eigenvalues and Eigenvectors; Orthogonality; Change of Basis; Eigenvalues: Further Applications and Computations; Complex Scalars; Solving Large Linear Systems MARKET: For all readers interested in linear algebra.

Table of Contents

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)
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)
Vector Spaces
Vector Spaces
Basic Concepts of Vector Spaces
Coordinatization of Vectors
Linear Transformations
Inner-Product Spaces (Optional)
Areas, Volumes, and Cross Products
The Determinant of a Square Matrix
Computation of Determinants and Cramer's Rule
Linear Transformations and Determinants (Optional)
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Two Applications
The Gram-Schmidt Process
Orthogonal Matrices
The Projection Matrix
The Method of Least Squares
Change of Basis
Coordinatization and Change of Basis
Matrix Representations and Similarity
Eigenvalues: Further Applications and Computations
Diagonalization of Quadratic Forms
Applications to Geometry
Applications to Extrema
Computing Eigenvalues and Eigenvectors
Complex Scalars
Algebra of Complex Numbers
Matrices and Vector Spaces with Complex Scalars
Eigenvalues and Diagonalization
Jordan Canonical Form
Solving Large Linear Systems
Considerations of Time
The LU-Factorization
Pivoting, Scaling, and Ill-Conditioned Matrices
Mathematical Induction
Two Deferred Proofs
LINTEK Routines
MATLAB Procedures and Commands Used in the Exercises
Table of Contents provided by Publisher. All Rights Reserved.

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