Course details

# Linear Algebra

ILG Acad. year 2019/2020 Winter semester 5 credits

Guarantor

Deputy Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

Hliněná Dana, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

Learning objectives

Why is the course taught

Prerequisite kwnowledge and skills

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).

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).

Syllabus of lectures

- Systems of linear homogeneous and non-homogeneous equations. Gaussian elimination.
- Matrices and matrix operations. Rank of the matrix. Frobenius theorem.
- The
*determinant*of a square matrix. Inverse and adjoint matrices. The methods of computing the determinant.The Cramer's Rule. - Numerical solution of systems of linear equations, iterative methods.
- 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.
- Linear mappings of vector spaces. Matrices of linear transformations.
- The transformation of the coordinates, homogeneous coordinates.
- Rotation, translation, symmetry and their matrices.
- The eigenvalues and eigenvectors. The orthogonal projections onto eigenspaces.
- The inner product. Orthonormal systems of vectors. Orthogonal projection and approximation. Gram-Schmidt orthogonalisation process.
- Conic sections.
- Quadratic forms and their classification using sections.
- Quadratic forms and their classification using eigenvectors.

Syllabus of numerical exercises

Progress assessment

- Evaluation of two homework assignments - groupwork (max 10 points).
- Evaluation of the two mid-term exams (max 30 points).

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.

Exam prerequisites

Schedule

Day | Type | Weeks | Room | Start | End | Lect.grp | Groups | Info |
---|---|---|---|---|---|---|---|---|

Mon | comp.lab | lectures | A113 | 10:00 | 11:50 | 1BIB 2BIA 2BIB | xx | Hlavičková |

Mon | comp.lab | lectures | A113 | 12:00 | 13:50 | 1BIA 2BIA 2BIB | xx | Hlavičková |

Tue | lecture | lectures | T12/2.173 | 13:00 | 14:50 | 1BIB 2BIA 2BIB | xx | Hlavičková |

Tue | comp.lab | lectures | T8/522 | 15:00 | 16:50 | 1BIB 2BIA 2BIB | xx | Hlavičková |

Tue | comp.lab | lectures | T8/522 | 17:00 | 18:50 | 1BIB 2BIA 2BIB | xx | Hlavičková |

Tue | exam | 2019-10-22 | D105 E112 | 18:00 | 20:50 | 1BIA 1BIB 2BIA 2BIB | 1. písemka | |

Wed | lecture | lectures | D0207 D105 | 12:00 | 13:50 | 1BIA 2BIA 2BIB | xx | Hliněná |

Wed | comp.lab | lectures | A113 | 14:00 | 15:50 | 1BIB 2BIA 2BIB | xx | Hliněná |

Thu | comp.lab | lectures | A113 | 10:00 | 11:50 | 1BIA 2BIA 2BIB | xx | Hliněná |

Thu | comp.lab | lectures | T8/522 | 11:00 | 12:50 | 1BIA 2BIA 2BIB | xx | Vítovec |

Thu | comp.lab | lectures | A113 | 12:00 | 13:50 | 1BIA 2BIA 2BIB | xx | Hliněná |

Thu | comp.lab | lectures | D0207 | 14:00 | 15:50 | 1BIA 2BIA 2BIB | xx | Hlavičková |

Thu | comp.lab | lectures | D0207 | 16:00 | 17:50 | 1BIA 2BIA 2BIB | xx | Hlavičková |

Fri | comp.lab | lectures | T8/503 | 07:00 | 08:50 | 1BIA 2BIA 2BIB | xx | Vítovec |

Fri | comp.lab | lectures | T8/503 | 09:00 | 10:50 | 1BIB 2BIA 2BIB | xx | Vítovec |

Fri | comp.lab | lectures | A113 | 13:00 | 14:50 | 1BIA 2BIA 2BIB | xx | Hlavičková |

Fri | comp.lab | lectures | A113 | 15:00 | 16:50 | 1BIB 2BIA 2BIB | xx | Hlavičková |

Fri | exam | 2019-11-22 | D0206 D105 E104 E105 E112 | 17:00 | 20:50 | 1BIA 1BIB 2BIA 2BIB | 2. písemka |

Course inclusion in study plans