Linear Algebra

by Fraleigh, John B.; Beauregard, Raymond A.

• ISBN13: 9780201526752
• ISBN10: 0201526751
• Edition: 3rd
• Format: Paperback
• Copyright: 1994-12-31
• Publisher: Pearson

Summary

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)

Determinants

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

Diagonalization

Two Applications

Orthogonality

Projections

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

Appendices

Mathematical Induction

Two Deferred Proofs

LINTEK Routines

MATLAB Procedures and Commands Used in the Exercises

Appendices

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