MATH262 LINEAR ALGEBRA II
| Course Code: | 2360262 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 9.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of the course the student will learn
- eigenvalue and eigenvector concept, their computation and uses.
- diagonalizability and diagonalization process
- Jordan canonical forms and rational canonical forms of linear operators/matrices
- inner product spaces, orthogonality; normal, unitary, self-adjoint, orthogonal linear operators /matrices .
Course Content
Characteristic and minimal polynomials of an operator, eigenvalues, diagonalizability, canonical forms, Smith normal form, Jordan and rational forms of matrices. Inner product spaces, norm and orthogonality, projections. Linear operators on inner product spaces, adjoint of an operator, normal, self adjoint, unitary and positive operators. Bilinear and quadratic forms.
Course Learning Outcomes
By the end of the course the student will learn
- definitions of eigenvalues, eigenvectors and their computations,
- diagonalizability, its uses and diagonalization process, simultaneous diagonalization,
- minimal and characteristic polynomials of linear operators/matrices, Cayley-Hamilton Theorem,
- definition of Jordan canonical form and rational canonical form,
- methods of finding Jordan canonical form of matrices,
- some applications about Jordan canonical forms,
- definition of inner product, norm and their basic properties,
- definition of orthogonal and orthonormal bases and their basic properties,
- definition and computation of orthogonal projection and orthogonalization,
- definition and basic properties of adjoints of linear operators on inner product spaces,
- definitions and basic properties of normal, orthogonal, unitary, self-adjoint linear operators/matrices.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution