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Elementary Linear Algebra: A Matrix Approach
Lawrence E. Spence, Illinois State University
Arnold J. Insel, Illinois State University
Stephen H. Friedberg, Illinois State University

ISBN-10: 0137167229
ISBN-13: 9780137167227

Publisher: Pearson
Copyright: 2000
Format: Cloth; 451 pp
Published: 09/07/1999

For a sophomore-level course in Linear Algebra.

Based on the recommendations of the LACSG, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications and less emphasis on abstraction than in a traditional course. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces.

This product accompanies:
Spence, Insel & Friedberg, Elementary Linear Algebra, 2/E

Matrix orientation.
- Allows instructors to present concepts more concretely. Ex.___

Emphasis on Euclidean n-space rather than abstract vector spaces.
- Builds student confidence by first introducing concepts in a familiar setting. Then when students are ready (mature), vector spaces are covered. Ex.___

A large number and variety of exercises (2200 in all)—Over 400 true/false questions, 100 practice problems (with solutions), theoretical exercises, and exercises that require the use of technology.
- Gives students the opportunity to test their understanding of basic concepts, practice performing important computations, delve more deeply into theory, formulate conjectures, and practice using technology. Ex.___

A large variety of applications.
- Shows students the breadth and power of linear algebra. Ex.___

Early introduction of the span and linear independence.
- Gives students a solid foundation in these key concepts by introducing them in familiar contexts early and by developing familiarity with them through computations. Ex.___

Interplay between matrices and linear transformations—Linear transformations are introduced in Ch. 2 and go hand-in hand with matrices.
- Provides motivation for several topics for which the linear transformation version is more natural than the matrix formulation. Ex.___

Optional sections that can be omitted without loss of continuity—e.g., Applications of Systems of Linear Equations; Applications of Matrix Multiplication; The LU Decomposition of a Matrix; Applications of Eigenvalues; Singular Value Decomposition; Rotations of R³.

Chapter reviews.

Boxed statements of important results.

Numbered (200) and unnumbered examples.

1. Matrices, Vectors, and Systems of Linear Equations.

Matrices and Vectors. Linear Combinations, Matrix-Vector Products, and Special Matrices. Systems of Linear Equations. Gaussian Elimination. Applications of Systems of Linear Equations. The Span of a Set Vectors. Linear Dependence and Independence. Chapter 1 Review.

2. Matrices and Linear Transformations.

Matrix Multiplication. Applications of Matrix Multiplication. Invertibility and Elementary Matrices. The Inverse of a Matrix. The LU Decomposition of a Matrix. Linear Transformations and Matrices. Composition and Invertibility of Linear Transformations. Chapter 2 Review.

3. Determinants.

Cofactor Expansion. Properties of Determinants. Chapter 3 Review.

4. Subspaces and Their Properties.

Subspaces. Basis and Dimension. The Dimension of Subspaces Associated with a Matrix. Coordinate Systems. Matrix Representations of Linear Operators. Chapter 4 Review.

5. Eigenvalues, Eigenvectors, and Diagonalization.

Eigenvalues and Eigenvectors. The Characteristic Polynomial. Diagonalization of Matrices. Diagonalization of Linear Operators. Applications of Eigenvalues. Chapter 5 Review.

6. Orthogonality.

The Geometry of Vectors. Orthonormal Vectors. Least-Squares Approximation and Orthogonal Projection Matrices. Orthogonal Matrices and Operators. Symmetric Matrices. Singular Value Decomposition. Rotations of R³ and Computer Graphics. Chapter 6 Review.

7. Vector Spaces.

Vector Spaces and their Subspaces. Dimension and Isomorphism. Linear Tranformations and Matrix Representations. Inner Product Spaces. Chapter 7 Review.

Appendix: Complex Numbers.

Introductory Linear Algebra [EASY TEXTS] (Mathematics)

Elementary Linear Algebra, 2/E
Spence, Insel & Friedberg
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ISBN-10: 0131871412 | ISBN-13: 9780131871410
Net price: $104.00 (What's this?)Brief Description

For a sophomore-level course in Linear Algebra.

Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces

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