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Elementary Linear Algebra: A Matrix Approach

Elementary Linear Algebra: A Matrix Approach


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About the Book

For a second year 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 spaces. *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. *Early introduction of the span and linear independence. *Interplay between matrices and linear transformations. *Provides motivation for several topics for which the linear transformation version is more natural than the matrix formulation. *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 R^3.

Table of Contents:


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.


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Product Details
  • ISBN-13: 9780137167227
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Height: 261 mm
  • No of Pages: 451
  • Sub Title: A Matrix Approach
  • Width: 210 mm
  • ISBN-10: 0137167229
  • Publisher Date: 08 Oct 1999
  • Binding: Hardback
  • Language: English
  • Spine Width: 23 mm
  • Weight: 1250 gr

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Elementary Linear Algebra: A Matrix Approach
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