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Course info
KMA / SMP
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Course description
Department/Unit / Abbreviation
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KMA
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SMP
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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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Seminar on Matrix Calculus
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Form of course completion
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Pre-Exam Credit
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Form of course completion
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Pre-Exam Credit
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Accredited / Credits
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Yes,
2
Cred.
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Type of completion
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-
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Type of completion
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-
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Time requirements
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Tutorial
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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NO
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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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0 / -
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0 / -
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Included in study average
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NO
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Winter semester
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100 / -
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72 / -
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27 / -
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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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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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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 |
S|N |
Periodicity |
každý rok
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Periodicita upřesnění |
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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 |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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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 aims at introducing the students to the basic terms of matrix theory and linear algebra and their application in solving basic problems.
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Requirements on student
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Credit: written exam.
Student fulfill requirements for the credit after he /she consults his/her test with the lecturer and presents his/her index for signing the credit.
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Content
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Week 1: Vectors, inner and vector product, vector algebra in 2D and 3D, mutual location of geometrical units.
Week2: Metrical exercises from vector algebra, transversal and distance of non-intersecting lines. Quadratic faces.
Week3: Polynomials, polynomial factorization, partial fractions.
Week4: Matrix operations and determinants.
Week5: Vector space, basis and dimension of a vector space, coordinates of a vector relative to a basis.
Week6: Rank of a matrix, matrix inverse.
Week7: Linear map (transformation): kernel and image and their dimension.
Week8: Linear map (transformation): associated matrix of a linear map, change of basis.
Week9: Systems of linear equations.
Week10: Eigenvalues and eigenvectors of a matrix, Jordan normal form of a matrix.
Week11: Inner product, orthogonal and orthonormal basis for a space (the Gram-Schmidt process), orthogonal projection of a vector on a subspace, method of least squares.
Week12: Quadratic forms, inertia of a quadratic form.
Week13: Written exam.
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Activities
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Fields of study
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Coursewarové stránky předmětu: https://portal.zcu.cz/portal/studium/courseware/kma/smp
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Guarantors and lecturers
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Guarantors:
RNDr. Jan Ekstein, Ph.D. (100%),
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Tutorial lecturer:
Doc. Ing. Roman Čada, Ph.D. (100%),
RNDr. Jan Ekstein, Ph.D. (100%),
Doc. RNDr. Přemysl Holub, Ph.D. (100%),
RNDr. Adam Kabela, Ph.D. (100%),
Jan Kaiser (100%),
Prof. RNDr. Tomáš Kaiser, DSc. (100%),
RNDr. Milena Šebková (100%),
RNDr. Blanka Šedivá, Ph.D. (100%),
RNDr. Mgr. Jakub Teska, Ph.D. (100%),
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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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Undergraduate study programme term essay (20-40)
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26
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Contact hours
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26
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Total
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52
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
vymezit pojem polynomu |
vymezit pojem vektoru |
poznat rovnice základních geometrických útvarů |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
použít základy analytické geometrie |
vyřešit jednoduché soustavy rovnic |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
vysvětlit pojem vektoru, matice, polynomu |
popsat pojem lineárního prostoru a lineárního zobrazení |
charakterizovat vlastní čísla a vlastní vektory |
Skills - skills resulting from the course: |
určit kořeny polynomu |
vypočítat determinant matice, matici inverzní a hodnost matice |
vyřešit soustavu algebraických rovnic |
určit vlastní čísla a vlastní vektory matice |
použít metodu nejmenších čtverců |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Skills demonstration during practicum |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
Skills demonstration |
Individual study |
Skills - the following training methods are used to achieve the required skills: |
Seminar |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Seminar |
Individual study |
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