CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

LINEAR ALGEBRA II | MAT204 | SPRING | 4+0 | Fac./ Uni. | C | 7 |

Learning Outcomes | 1-To be able to describe linear transformations 2-To be able to find representative of a linear transformation relative to the given basis 3-To be able to find the representative of a linear transformation related to a second base from the first one 4-To be able to find some particular matrices respresenting a linear transformation 5-To be able to determine basis of dual space of a real vector space 6-To be able to explain the fundamental concepts of inner product space |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 6 | 84 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 200 | |||

Total Workload (hours) / 30 (s) | 6,67 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Vector spaces over a field | |

2 | Inner product spaces | |

3 | Linear transformation, kernel and range | |

4 | Matrix representation of linear transformations | |

5 | Eigenvalues and eigenvectors, characteristic polynomial | |

6 | Cayley-Hamilton Theorem, minimal polynomial | |

7 | Diagonalization of linear transformations | |

8 | Direct sums of subspaces | |

9 | Orthogonal transformations | |

10 | Primary decomposition | |

11 | Reduction to triangular form | |

12 | Reduction to Jordan form | |

13 | Dual spaces I | |

14 | Dual spaces II |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Faruk KARAASLAN |

Instructors | - |

Assistants | - |

Resources | 1. Elementary Linear Algebra, 8th Edition, B. Kolman, D.R. Hill, Prentice-Hall, New Jersey, 2004 2. Basic Linear Algebra, Second Edition, T.S. Blyth, E.F. Robertson, Springer 2002 |

Supplementary Book | Linear Algebra, 2nd Edition, K. Hoffman, R. Kunze, Prentice-Hall, New Jersey, 1971 |

Document | - |

Goals | The aim of this course is introduce the students linear transformations theory by using Linear Algebra knowledge which is learned previous semester. To teach the student concept of Linear transformations, represenation by matrices, special forms (diagonal, triangular), and besides these, to teach inner products and dual spaces. to the very heart of the subject including topics such as inner product spaces and linear mappings on them, canonical (diagonal, triangular, Jordan, and rational) matrix forms of linear mappings, bilinear and quadratic forms. |

Content | Vector spaces over arbitrary fields. Inner product spaces. Linear transformations, kernel and image. Matrix representations of linear transformations. Eigen value, eigen vector, characteristic polynomial. Cayley Hamilton theorem, minimal polynomial. Diagonalization of a linear transformation. Direct sums of subspaces. Projection transformations. Primary decomposition. Triangulization of a linear transformation. Jordan form. Dual spaces. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 5 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 3 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 2 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 3 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 3 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | - |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 3 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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