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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Linear Algebra 2

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Code Completion Credits Range Language
01LAL2 Z,ZK 4 2P+2C Czech
Vztahy:
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.
Garant předmětu:
Lubomíra Dvořáková
Lecturer:
Petr Ambrož, Lubomíra Dvořáková
Tutor:
Petr Ambrož, Lubomíra Dvořáková, Jiří Franc, Tomáš Hrdina, David Kramár, David Krejčiřík, Václav Růžek
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:

Knowledge of Linear algebra 1 (LAL1) is demanded. Only students who have passed the exam in LAL1 are admitted to the exam in LAL2.

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 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-15
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