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Course info
KMA / MKE
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Course description
Department/Unit / Abbreviation
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KMA
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MKE
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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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,
3
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]
Tutorial
1
[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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280 / -
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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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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 |
0
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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 |
No
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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 linear algebra, mainly of matrix calculus, and their application.
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Requirements on student
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passing a final test, active participation at lectures and seminars
It is stated by the garant that Pre-Exam Credit is not admitted if repeated entry (see čl. 24, odst. 3 SZŘ ZČU)
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Content
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1st week - Complex numbers - definition, Gaussian plane, calculus, trigonometric and exponential form of a complex number, solving quadratic equations in complex domain
2nd-3rd week - Polynomials - calculus, roots of a polynomial, Horner scheme, factorization of a polynomial, decomposition of a rational function into partial fractions
4th week - Martix - basic definitions, calculus, rank of a matrix
5th-6th week - System of linear algebraic equations - matrix representation, existence of a solution, Gaussian elimination algorithm, inverse matrix
7th-8th week - Linear vector space - linear independence of elements of LVS, basis and dimension of LVS, coordinates of an element of LVS in a given basis
9th week - Determinant of a matrix - calculation, usage for solving a system of linear algebraic equations
10th-11th week - Eigenvalues and eigenvectors of a matrix, Jordan canonical form of a matrix, similarity of matrices
12th-13th week - Inner product - orthogonal projection, least square method
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Activities
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Fields of study
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https://courseware.zcu.cz/portal/studium/courseware/kma/mke
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Guarantors and lecturers
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-
Guarantors:
Doc. RNDr. Přemysl Holub, Ph.D. ,
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Lecturer:
RNDr. Jan Ekstein, Ph.D. (100%),
RNDr. Milena Šebková (100%),
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Tutorial lecturer:
RNDr. Jan Ekstein, Ph.D. (100%),
Doc. RNDr. Přemysl Holub, Ph.D. (100%),
Mgr. Mária Skyvová (100%),
RNDr. Milena Šebková (100%),
RNDr. Mgr. Jakub Teska, Ph.D. (100%),
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Literature
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Time requirements
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Full-time form of study
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Activities
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Time requirements for activity [h]
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Preparation for comprehensive test (10-40)
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39
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Contact hours
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39
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Total
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78
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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: |
A knowledge of mathematics and its application taught at ordinary secondary schools are expected |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
work with terms commonly taught at ordinary secondary schools |
strandard simplification of algebraic expressions, solving of linear and quadratic equations |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
define basic terms from the following fields: Polynomials, Matrices, Linear vector space |
Skills - skills resulting from the course: |
among others to solve the following problems: factorization of a polynomial, decomposition of a rational function into partial fractions; system of linear algebraic equations, rank and determinant of a matrix, inverse matrix, eigenvalues and eigenvectors of a matrix; the Least square method |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Continuous assessment |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Continuous assessment |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
Continuous assessment |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Interactive lecture |
Practicum |
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