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Elementary Linear Algebra : A Matrix Approach
ISBN: 9780137167227 | 0137167229
Edition: 2ndFormat: Hardcover
Publisher: PRENTICE HALL
Pub. Date: 1/1/2008
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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 ... MORE
1. Matrices, Vectors, and Systems of Linear Equations.
2. Matrices and Linear Transformations.
3. Determinants.
4. Subspaces and Their Properties.
5. Eigenvalues, Eigenvectors, and Diagonalization.
6. Orthogonality.
7. Vector Spaces.
Appendix: Complex Numbers.
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 ... MORE
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 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.
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