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Course info
KMA / 7TEMA
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Course description
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Department/Unit / Abbreviation
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KMA
/
7TEMA
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Matrix Theory
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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lecture
2
[Hours/Week]
practical class
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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4 / -
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0 / 0
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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not determined
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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| No. of hours of on-premise lessons |
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Evaluation scale |
A|B|C|D|E|F |
| Periodicity |
every year
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| Specification periodicity |
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Fundamental theoretical course |
No
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| Fundamental course |
Yes
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| Fundamental theoretical course |
No
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| Evaluation scale |
A|B|C|D|E|F |
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Substituted course
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None
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Preclusive courses
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KMA/TEMAT
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The course is devoted to advanced properties of matrices and to their applications.
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Requirements on student
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The course is completed with an exam, which consists of a written test (aimed at solving problems and examining basic definitions and theorems) and an oral part (devoted to discussing the test and to theoretical questions).
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Content
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1. Elementary operations with matrices.
2. Matrix norms.
3. Eigenvalues and eigenvectors.
4. Matrix similarity. Diagonalization.
5. Projections. Spectral decomposition.
6. Jordan normal form.
7. Matrix functions.
8. Singular value decomposition.
9. Pseudoinverse.
9. Special classes of matrices and their properties.
10. Positive matrices. Perron-Frobenius theorem.
12. Examples of applications of matrices in mathematics and physics.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Being present in classes
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52
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Consultation of work with the teacher/tutor (incl. electronic)
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10
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Self-tutoring
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10
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Scientific text studying in the Czech language
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20
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Continuous tasks completion (incl. correspondence tasks)
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24
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Scientific text studying in a foreign language
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10
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Preparation for an exam
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24
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Total
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150
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Prerequisites
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Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
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| The student has a basic knowledge of linear algebra. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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| Student knows matrix norms and relations between them, understands the eigenvalue and eigenvector problem, knows and understands spectral decomposition, understands the notion of matrix similarity, is familiar with Jordan normal form of a matrix and its derivation, knows the Perron-Frobenius theorem, understands matrix functions, knows examples of practical applications of matrices, and is able to study related specialized literature. |
Skills - skills resulting from the course: |
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| Student can localize eigenvalues, is able to find spectral decomposition of a given matrix, can transform a matrix to its Jordan form, is able to compute matrix functions and to use it for solving practical problems. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| Continuous analysis of student´s achievements |
| Dialogue |
| Written examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| Monologic (explanation, lecture, briefing) |
| Dialogic (discussion, dialogue, brainstorming) |
| Working with text (coursebook, book) |
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