Linear Algebra 2

Relations:

The course 01LAL2 can be graded only after the course 01LALZ has been successfully completed.

In order to register for the course 01ANA3, the student must have successfully completed the course 01LAL2.

Course guarantor:

Lubomíra Dvořáková

Lecturer:

Petr Ambrož, Lubomíra Dvořáková

Tutor:

Petr Ambrož, Daniela Černá, Lubomíra Dvořáková, Jiří Franc, Herman Goulet-Ouellet, Veronika Hendrychová, Tomáš Hrdina, Mikuláš Kučera, Václav Růžek, Filip Záhon Persidský

Supervisor:

Department of Mathematics

Synopsis:

Outline:

1. Inverse matrix and operator.

2. Permutation and determinant.

3. Spectral theory (eigenvalue, eigenvector, diagonalization).

4. Hermitian and quadratic forms.

5. Scalar product and orthogonality.

6. Metric geometry.

7. Riesz theorem and adjoint operator.

Outline of the exercises:

1. Methods for calculation of inverse matrices.

2. Methods of calculation of determinants.

3. Calculation of eigenvalues and eigenvectors.

4. Hermitian and quadratic forms. Canonical form.

5. Scalar product and orthogonality. Calculation of orthogonal complements.

6. Geometry exercises and examples.

7. Adjoint operators.

Requirements:

Credit from 01LAL2 is awarded for active participation (maximum 2 absences).

The exam has a written and oral part.

The written part of the exam also consists of a practical part and a theoretical part. Each of these parts is evaluated at most 100%.

If a student has obtained at least 50% of points from each of the control tests written during the semester, he can use the opportunity at the beginning of each of the examination terms to have the average of his results from the control tests recognized as the result of the practical part of the written exam, which he does not take in such a case.

If the result of any part of the written exam is less than 50%, the exam ends, the student is classified with a grade of F.

If the result of both parts of the written exam is 50% or more, the points from the instructor for the work in the semester are added to the result of the practical part of the exam (1 point = 1 percent) and the result of the written exam is then given by the arithmetic average of the percentage evaluation of its practical and theoretical parts and is graded according to the standard classification scale (see Article 11 of the CTU Study and Examination Regulations). With the grade from the written exam, the student then proceeds to the oral exam, its form (the difficulty of the questions asked) is based on the result of the written exam.

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] L. Dvořáková: Linear algebra 2, textbook, available online on request

[2] T. M. Apostol: Linear Algebra: A First Course with Applications to Differential Equations, John Wiley & Sons, 2014

[3] R. C. Penney: Linear algebra and applications, John Wiley &Sons, 2015

Recommended references:

[3] G. Strang: Introduction to Linear Algebra, Wesley Cambridge Press, 2016

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Aplikovaná algebra a analýza (compulsory course in the program)
• Aplikace informatiky v přírodních vědách (compulsory course in the program)
• Aplikované matematicko-stochastické metody (compulsory course in the program)
• Jaderné inženýrství - Aplikovaná fyzika ionizujícího záření (PS)
• Fyzikální inženýrství - Fyzikální inženýrství materiálů (PS)
• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (PS)
• Fyzikální inženýrství - Inženýrství pevných látek (PS)
• Jaderná a částicová fyzika (compulsory course in the program)
• Jaderné inženýrství - Jaderné reaktory (PS)
• Fyzikální inženýrství - Laserová technika a fotonika (PS)
• Matematické inženýrství - Matematická fyzika (PS)
• Matematické inženýrství - Matematická informatika (PS)
• Matematické inženýrství - Matematické modelování (PS)
• Kvantové technologie (compulsory course in the program)
• jaderné inženýrství - Radioaktivita v životním prostředí (PS)
• Vyřazování jaderných zařízení z provozu (compulsory course in the program)
• Physical Engineering - Physical Engineering od Materials (PS)
• Mathematical Engineering - Mathematical Informatics (PS)