Course Description
The Jordan canonical form. Bilinear and quadratic forms. Matrix analysis of differential equations. Variational principles and perturbation theory, Weyl’s inequalities, Gershgorin’s theorem, perturbations of the spectrum, vector norms, matrix norms, the condition number of a matrix.
Course Objectives & Outcomes
Objectives:
- Give to the student the fundamental definitions and concepts of Applied Matrix theory.
- Equip the student with necessary knowledge and skills to enable him to apply Variational principles and perturbation theory.
- Develop skills in applyingthe Jordan Canonical Form.
- Develop skills in applying the Gershgorin’s theorem for estimating Eigenvalues.
- Enable the student to apply their knowledge of Applied Matrix theory to problems in other areas.
Outcomes: Upon successful completion of this course,the student will be able to:
- Discuss the essential concepts of Applied Matrix theory.
- Usethe concepts and knowledge needed to obtain solution of linear system.
- Define the concepts of vector norms, matrix norms, and how to find the condition number of a matrix.
- Apply the perturbation theorem and variational principles for determine Eigenvalues iteratively.
- Explain numerical methods to solve linear algebra problems.
- Apply his knowledge of Applied Matrix theoryto problems in other areas.
References
1. Joel. N. F., (2000), Matrix theory, dover publications.ISBN-13: 000-0486411796,
ISBN-10: 0486411796.
2. Gilbert, S., (2006), Linear algebra and its application, 4th edition Thomson.ISBN-13: 978-0030105678, ISBN-10: 0030105676
3. Carl, M., (2000), Matrix analysis and applied linear algebra, Siam, ISBN-13: 978-0898714548, ISBN-10: 0898714540
Course ID: MATH 504
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 2 | 2 | 4 | MATH 405 |
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