This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and nature of Linear Spaces and of Linear Transformations. Almost every chapter has three sections: a lecture followed by problems, theoretical and mathematical enrichment, and applications to and from Linear Algebra. KEY TOPICS: Specific chapter topics cover linear transformations; row reduction; linear equations; subspaces; linear dependence, bases, and dimension; composition of maps, matrix inverse and transpose; coordinate vectors, basis change; determinants, l-matrices; matrix eigenvalues; orthogonal bases and orthogonal matrices; symmetric and normal matrix eigenvalues; singular values; and basic numerical linear algebra techniques. MARKET: For individuals in fields related to economics, engineering, science, or mathematics.
Table of contents
Introduction (Mathematical Preliminaries, Vectors, Sets, and Symbols).
1. Linear Transformations.
3. Linear Equations.
5. Linear Dependence, Bases, and Dimension.
6. Composition of Maps, Matrix Inverse.
7. Coordinate Vectors, Basis Change.
8. Determinants, Lambda-Matrices.
9. Matrix Eigenvalues and Eigenvectors.
10. Orthogonal Bases and Orthogonal Matrices.
11. Symmetric and Normal Matrix Eigenvalues.
12. Singular Values.
13. Basic Numerical Linear Algebra Techniques.
*14. Nondiagonalizable Matrices, the Jordan Normal Form.
Appendix A (Complex Numbers and Vectors).
Appendix B (Finding Integer Roots of Integer Polynomials).
Appendix C (Abstract Vector Spaces).
*Appendix D (Inner Product Spaces).
List of Photographs.
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