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Courses on linear algebra and numerical analysis need each other. Often NA courses have some linear algebra topics, and LA courses mention some topics from numerical analysis/scientific computing. This text merges these two areas into one introductory undergraduate course. It assumes students have had multivariable calculus. A second goal of this text is to demonstrate the intimate relationship of linear algebra to applications/computations.
A rigorous presentation has been maintained. A third reason for writing this text is to present, in the first half of the course, the very important topic on singular value decomposition, SVD. This is done by first restricting consideration to real matrices and vector spaces. The general inner product vector spaces are considered starting in the middle of the text.
The text has a number of applications. These are to motivate the student to study the linear algebra topics. Also, the text has a number of computations. MATLAB® is used, but one could modify these codes to other programming languages. These are either to simplify some linear algebra computation, or to model a particular application.
List of contents
1. Solution of AX = d. 2. Matrix Factorizations. 3. Least Squares and Normal Equations. 4. Ax = d with m 5. Orthogonal Subspaces and Bases. 6. Eigenvectors and Orthonormal Basis. 7. Singular Value Decomposition. 8. Three Applications of SVD. 9. Pseudoinverse of A. 10. General Inner Product Vector Spaces. 11. Iterative Methods. 12. Nonlinear Problems and Least Squares.
Summary
Courses on linear algebra and numerical analysis need each other. Often NA courses have some linear algebra topics, and LA courses mention some topics from numerical analysis/scientific computing. This text merges these two areas into one introductory undergraduate course. It assumes students have had multivariable calculus.
