Description
Outstanding features include:
• Early coverage of vector spaces, providing the abstract theory necessary to understand applications
• Exercises that range from routine to more challenging, extending the concepts and techniques by asking students to construct complete arguments
• Numerous examples designed to develop intuition and prepare readers to think conceptually about topics as they are introduced
• Fact summaries to end each chapter that use nontechnical language to recapitulate details and formulas
“The book is very well organized. We appreciate its thoroughness.” — Kristina Sampson, Lone Star College
Systems of Linear Equations / Matrices and Elementary Row Operations / Matrix Algebra / The Inverse of a Square Matrix / Matrix Equations / Determinants / Elementary Matrices and LU Factorization / Applications of Systems of Linear Equations
2. Linear Combinations and Linear Independence
Vectors in Rn / Linear Combinations / Linear Independence
3. Vector Spaces
Definition of a Vector Space / Subspaces / Basis and Dimension / Coordinates and Change of Basis / Application: Differential Equations
4. Linear Transformations
Linear Transformations / The Null Space and Range / Isomorphisms / Matrix Representation of a Linear Transformation / Similarity / Application: Computer Graphics
5. Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors / Diagonalization / Application: Systems of Linear Differential Equations / Application: Markov Chains
6. Inner Product Spaces
The Dot Product on Rn / Inner Product Spaces / Orthonormal Bases / Orthogonal Complements / Application: Least Squares Approximation / Diagonalization of Symmetric Matrices / Application: Quadratic Forms / Application: Singular Value Decomposition
Reviews
There are no reviews yet.