457-0532/01 – Linear Algebra with Matlab (LAM)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | prof. Ing. Tomáš Kozubek, Ph.D. | Subject version guarantor | prof. Ing. Tomáš Kozubek, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2007/2008 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
To expand the knowledge of the students using Matlab by concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems.
Teaching methods
Lectures
Seminars
Project work
Summary
Advanced concepts of linear algenra are key ingredients in solving of many engineering problems such as signal analysis, implemetation of search engins, optimal control or numerical solution of differential equations. In this course, the students can expand their knowledge of linear algebra using Matlab by working knowledge of concepts that are important in understanding of modern methods used in informatics and numerical solution of engineering problems with a special stress on matrix decompositions and the spectral theory.
Compulsory literature:
Recommended literature:
Příklady z lineární algebry II a materiál k domácímu projektu.
Way of continuous check of knowledge in the course of semester
Conditions for credit:
Project (minimum 15 points).
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Introduction to MATLAB (overview of toolboxes and functions, help, basic elements, editing of the n-dimensional arrays).
MATLAB programming (control flow statements, 2D and 3D graphics).
Advanced MATLAB functions (graphical user interface).
Analytic geometry (computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures (band, profile, row compressed, column compressed).
Solution of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Gauss elimination (row and column versions, pivotization).
LU and Choleski decomposition (row and column versions, pivotization).
Reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
QR decomposition (Givens and Householder transforms).
Eigenvalues and spectral decomposition (QR and LR algorithms, shift).
Singular decomposition, pseudoinverse.
Lanczos method and conjugate gradient method.
Project presentation.
Exercises:
Introduction to MATLAB, functions overview, editing of the n-dimensional arrays.
MATLAB programming techniques, the use of the control flow statements, 2D and 3D graphic functions).
Graphical user interface implementation.
Computation of the inclinations and distances in 2D and 3D).
Sparse matrix structures implementation (band, profile, row compressed, column compressed).
Solvers of the linear algebraic systems (nonsingular, underdetermined and overdetermined systems).
Solution of the linear algebraic system using Gauss elimination (row and column versions, pivotization).
Solution of the linear algebraic system using LU and Choleski decomposition (row and column versions, pivotization).
Application of the reordering algorithms (SYMAMD, COLAMD, SLOAN, RCM).
The use of the QR decomposition (implementation, Givens and Householder transforms, applications).
Computation of the eigenvalues and spectral decomposition (implementation, QR and LR algorithms, shift, applications).
Computation of the singular decomposition and pseudoinverse (implementation, application).
Lanczos method and conjugate gradient method (implementation, applications).
Project presentation.
Projects:
Application oriented project in MATLAB (max. 30 points).
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction