Title:

Linear Algebra

Code:ILG
Ac.Year:2019/2020
Sem:Winter
Curriculums:
ProgrammeField/
Specialization
YearDuty
BIT-1stCompulsory
IT-BC-3BIT1stCompulsory
Language of Instruction:Czech
Credits:5
Completion:credit+exam (written)
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:2626000
 ExamsTestsExercisesLaboratoriesOther
Points:60300010
Guarantor:Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Deputy guarantor:Hlavičková Irena, Mgr., Ph.D. (DMAT)
Lecturer:Hlavičková Irena, Mgr., Ph.D. (DMAT)
Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Instructor:Hlavičková Irena, Mgr., Ph.D. (DMAT)
Hliněná Dana, doc. RNDr., Ph.D. (DMAT)
Vítovec Jiří, Mgr., Ph.D. (DMAT)
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
Substitute for:
Discrete Mathematics (IDA), DMAT
Schedule:
DayLessonWeekRoomStartEndLect.Gr.Groups
Moncomp.lab - HlavičkoválecturesA113 10:0011:501BIB 2BIA 2BIB xx
Moncomp.lab - HlavičkoválecturesA113 12:0013:501BIA 2BIA 2BIB xx
Tuelecture - HlavičkoválecturesT12/2.173 13:0014:501BIB 2BIA 2BIB xx
Tuecomp.lab - HlavičkoválecturesT8/522 15:0016:501BIB 2BIA 2BIB xx
Tuecomp.lab - HlavičkoválecturesT8/522 17:0018:501BIB 2BIA 2BIB xx
Wedlecture - HliněnálecturesD0207 D105 12:0013:501BIA 2BIA 2BIB xx
Wedcomp.lab - HliněnálecturesA113 14:0015:501BIB 2BIA 2BIB xx
Thucomp.lab - HliněnálecturesA113 10:0011:501BIA 2BIA 2BIB xx
Thucomp.lab - VítoveclecturesT8/522 11:0012:501BIA 2BIA 2BIB xx
Thucomp.lab - HliněnálecturesA113 12:0013:501BIA 2BIA 2BIB xx
Thucomp.lab - HlavičkoválecturesD0207 14:0015:501BIA 2BIA 2BIB xx
Thucomp.lab - HlavičkoválecturesD0207 16:0017:501BIA 2BIA 2BIB xx
Fricomp.lab - VítoveclecturesT8/503 07:0008:501BIB 2BIA 2BIB xx
Fricomp.lab - VítoveclecturesT8/503 09:0010:501BIB 2BIA 2BIB xx
Fricomp.lab - HlavičkoválecturesA113 13:0014:501BIA 2BIA 2BIB xx
Fricomp.lab - HlavičkoválecturesA113 15:0016:501BIB 2BIA 2BIB xx
Friexam - 1. písemka2019-10-25D0206 D105 E104 E105 E112 17:0020:501BIA 1BIB 2BIA 2BIB
Friexam - 2. písemka2019-11-22D0206 D105 E104 E105 E112 17:0020:501BIA 1BIB 2BIA 2BIB
 
Learning objectives:
  The students will get familiar with elementary knowledge of linear algebra, which is needed for informatics applications. Emphasis is placed on mastering the practical use of this knowledge to solve specific problems.
Description:
  Matrices and determinants. Systems of linear equations. Vector spaces and subspaces. Linear representation, coordinate transformation. Own values and own vectors. Quadratic forms and conics.
Knowledge and skills required for the course:
  Secondary school mathematics.
Learning outcomes and competencies:
  The students will acquire an elementary knowledge of linear algebra and the ability to apply some of its basic methods in computer science.
Why is the course taught:
  Linear algebra is one of the most important branches of mathematics for engineers, regardless of their specialization, as it deals with both specific computational procedures and abstract concepts, which are useful for describing technical problems. The knowledge gained in the course is applied by graduates where engineering problems are written in  matrices, vectors and linear equations. The mastering of the basic concepts and their context will facilitate for further study and development of the chosen field.
Syllabus of lectures:
 
  1. Systems of linear homogeneous and non-homogeneous equations. Gaussian elimination.
  2. Matrices and matrix operations. Rank of the matrix. Frobenius theorem.
  3. The determinant of a square matrix. Inverse and adjoint matrices. The methods of computing the determinant.The Cramer's Rule.
  4. Numerical solution of systems of linear equations, iterative methods.
  5. The vector space and its subspaces. The basis and the dimension. The coordinates of a vector relative to a given basis. The sum and intersection of vector spaces.
  6. Linear mappings of vector spaces. Matrices of linear transformations.
  7. The transformation of the coordinates, homogeneous coordinates.  
  8. Rotation, translation, symmetry and their matrices.
  9. The eigenvalues and eigenvectors. The orthogonal projections onto eigenspaces.
  10. The inner product. Orthonormal systems of vectors. Orthogonal projection and approximation. Gram-Schmidt orthogonalisation process.
  11. Conic sections.
  12. Quadratic forms and their classification using sections.
  13. Quadratic forms and their classification using eigenvectors.
Syllabus of numerical exercises:
 Examples of tutorials are chosen to suitably complement the lectures.
Fundamental literature:
 
  • Bečvář, J., Lineární algebra, matfyzpress, Praha, 2005. (in Czech).
  • Bican, L., Lineární algebra, SNTL, Praha, 1979. (in Czech).
  • Birkhoff, G., Mac Lane, S. Prehľad modernej algebry, Alfa, Bratislava, 1979. (in Slovak).
  • Havel, V., Holenda, J., Lineární algebra, STNL, Praha 1984. (in Czech).
  • Hejný, M., Zaťko, V, Kršňák, P., Geometria, SPN, Bratislava, 1985. (in Slovak).
  • Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
  • Kolman B., Introductory Linear Algebra, Macmillan Publ. Comp., New York 1993.
  • Neri, F., Linear algebra for computational sciences and engineering, Springer, 2016.
  • Olšák, P., Úvod do algebry, zejména lineární. FEL ČVUT, Praha, 2007. (in Czech).
Study literature:
 
  • Bečvář, J., Lineární algebra, matfyzpress, Praha, 2005. (in Czech).
  • Kovár, M.,  Maticový a tenzorový počet, FEKT VUT, Brno, 2013. (in Czech).
  • Olšák, P., Úvod do algebry, zejména lineární. FEL ČVUT, Praha, 2007. (in Czech).
Controlled instruction:
  
  • Participation in lectures in this course is not controlled.
  • The knowledge of students is tested at exercises; including two homework assignments worth for 5 points each, at two midterm exams for 15 points each, and at the final exam for 60 points.
  • If a student can substantiate serious reasons for an absence from an exercise, (s)he can either attend the exercise with a different group (please inform the teacher about that) or ask his/her teacher for an alternative assignment to compensate for the lost points from the exercise.
  • The passing boundary for ECTS assessment: 50 points.
Progress assessment:
  
  • Evaluation of two homework assignments - groupwork (max 10 points).
  • Evaluation of the two mid-term exams (max 30 points).
Exam prerequisites:
  The minimal total score of 10 points gained out of the mid-term exams. Plagiarism and not allowed cooperation will cause that involved students are not classified and disciplinary action may be initiated.
 

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