Elementary Linear Algebra: A Matrix Approach, 1/e
Lawrence E. Spence
Arnold J. Insel
Stephen H. Friedberg, all of Illinois State University
Published September, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 477 pp.
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Introductory Linear Algebra-Mathematics
Linear Algebra-Mechanical Engineering
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.
Emphasis on Euclidean n-space rather than abstract vector
- Allows instructors to present concepts more concretely.
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.
- Builds student confidence by first introducing concepts
in a familiar setting. Then when students are ready (mature), vector
spaces are covered.
A large variety of applications.
- 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
Early introduction of the span and linear independence.
- Shows students the breadth and power of linear algebra.
Interplay between matrices and linear transformationsLinear
transformations are introduced in Ch. 2 and go hand-in hand with matrices.
- Gives students a solid foundation in these key concepts
by introducing them in familiar contexts early and by developing familiarity
with them through computations.
Optional sections that can be omitted without loss of
continuitye.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 R^3.
- Provides motivation for several topics for which the
linear transformation version is more natural than the matrix formulation.
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
Cofactor Expansion. Properties of Determinants. Chapter
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.
The Geometry of Vectors. Orthonormal Vectors. Least-Squares
Approximation and Orthogonal Projection Matrices. Orthogonal Matrices
and Operators. Symmetric Matrices. Singular Value Decomposition. Rotations
of R^3 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.