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Main menu for Browse IS/STAG
Course info
KMA / LAA
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Course description
Department/Unit / Abbreviation
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KMA
/
LAA
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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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Linear Algebra
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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,
5
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
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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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
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Occ/max
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|
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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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YES
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Winter semester
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305 / -
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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 + Summer
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Semester taught
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Winter + Summer
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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
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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 |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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KMA/LA and KMA/LA-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
,
XLS
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Course objectives:
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The course is intended as an introduction to linear algebra.
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Requirements on student
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Credit requirements: full-time study - written tests, combined form of study - homework assignments (see http://portal.zcu.cz - CourseWARE)
Exam: written test, orals.
Combined form of study - for requirements see http://portal.zcu.cz - CourseWARE
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Content
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1. Complex numbers, fields. Polynomials, rings. Horner scheme, polynomial factorization.
2. Vector space, linear dependence and independence, basis and dimension of vector space, coordinates of vector relative to basis
3. Matrices, determinant of matrix and its basic properties, determinant expansion
4. Gaussian elimination. Fast calculation of determinants. Vector spaces associated with matrix. Rank of matrix, calculation of rank using determinants
5. Matrix inverse, Gauss-Jordan elimination, calculation of matrix inverse using determinants
6. Linear transformation, kernel and image and their dimensions, matrix of linear transformation and its properties. Fundamental Theorem of Linear Algebra.
7. Inverse linear transformation, linear transformation composition and its matrix, vector space isomorphism, change of basis and change-of-basis matrix
8. Systems of linear equations, homogeneous and non-homogeneous systems of equations, linear systems with invertible coefficient matrix, Cramer's rule
9. Eigenvalues and eigenvectors of matrix, generalized eigenvectors. Similarity of matrices. Jordan normal form of matrix. Matrix functions
10. Metric, norm, inner product and their properties. Euclidean and unitary spaces. Orthogonal and orthonormal basis for a vector space
11. Gram-Schmidt process, orthogonal projection onto subspace. QR decomposition of a matrix.
12. Linear least squares regression. Linear forms. Multilinear forms. Quadratic forms and real valued symmetric matrices. Definiteness of a matrix.
13. Inertia of quadratic form, Sylvester's law of inertia for quadratic forms. Quadratic forms and optimization.
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Activities
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Fields of study
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Pro studenty jsou k dispozici kompletní studijní materiály, scany přednášek a další pomocné materiály na stránce https://portal.zcu.cz/portal/studium/courseware/kma/laa
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Guarantors and lecturers
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Guarantors:
Doc. RNDr. Přemysl Holub, Ph.D. ,
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Lecturer:
Doc. RNDr. Přemysl Holub, Ph.D. (100%),
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Tutorial lecturer:
RNDr. Jan Ekstein, Ph.D. (100%),
Doc. RNDr. Přemysl Holub, Ph.D. (100%),
Mgr. Martin Kopřiva (100%),
Bc. Kateřina Krejčíková (100%),
Bc. Petra Melicharová (100%),
RNDr. Milena Šebková (100%),
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Literature
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Basic:
Anton, H.; Rorres, Ch. Elementary Linear Algebra: Applications Version. Wiley, 2013. ISBN 978-1118434413.
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Basic:
Tesková, Libuše. Lineární algebra. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-797-1.
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Basic:
Tesková, Libuše. Sbírka příkladů z lineární algebry. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7043-263-2.
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Extending:
Motl, Luboš. Pěstujeme lineární algebru. 2. vyd. Praha : Univerzita Karlova, 1999. ISBN 80-7184-815-8.
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Extending:
Motl, Luboš; Zahradník, Miloš. Pěstujeme lineární algebru. Univerzita Karlova, 2002. ISBN 80-246-0421-3.
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Recommended:
Demlová, Marie; Nagy, Jozef. Algebra. 2. vyd. Praha : SNTL, 1985.
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Recommended:
Olver, Peter J.; Shakiban, Chehrzad. Applied Linear Algebra. Springer International Publishing AG, part of Springer Nature, 2018. ISBN 978-3-319-91040-6.
( DOI: https://doi.org/10.1007/978-3-319-91041-3 )
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Recommended:
Bican, Ladislav. Linární algebra a geometrie. Academia, 2009. ISBN 978-80-200-1707-9.
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Recommended:
Axler, Sheldon. Linear Algebra Done Right. Springer International Publishing, 2015. ISBN 978-3-319-11079-0.
( DOI: https://doi.org/10.1007/978-3-319-11080-6 )
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Recommended:
Havel, Václav; Holenda, Jiří. Lineární algebra. 1. vyd. Praha : SNTL, 1984.
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Recommended:
Bečvář, Jindřich. Lineární algebra. MatfyzPress, 2020. ISBN 978-80-7378-378-5.
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Recommended:
Hladík, Milan. Lineární algebra (nejen) pro informatiky. MatfyzPress, 2019. ISBN 9788073783921.
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On-line library catalogues
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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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Preparation for an examination (30-60)
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54
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Preparation for formative assessments (2-20)
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12
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Contact hours
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65
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Total
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131
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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: |
to explain the concept of a vector |
to define the concept of a function |
to identify equations of basic geometric configurations |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
to use basics of analytic geometry |
to solve elementary systems of equations |
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: |
to explain the concept of a vector and matrix |
to describe the concept of a vector space |
to describe the concept of a linear transformation |
to characterize eigenvalues and eigenvectors of a matrix |
Skills - skills resulting from the course: |
to find roots of polynomials in one variable |
to calculate determinant of a matrix, matrix inverse and rank of matrix |
to solve systems of linear algebraic equations |
to find eigenvalues and eigenvectors of a matrix |
to use the least squares method |
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: |
Oral exam |
Written exam |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Written exam |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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