Linear algebra
General data
Course ID: | 1000-711ALI |
Erasmus code / ISCED: | (unknown) / (unknown) |
Course title: | Linear algebra |
Name in Polish: | Algebra liniowa |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Obligatory courses for 1st year Bioinformatics |
ECTS credit allocation (and other scores): |
4.50
|
Language: | Polish |
Type of course: | obligatory courses |
Short description: |
Introduction to methods of solving systems of linear equations and to the basics of matrix and metric spaces theory. |
Full description: |
1. Gauss elimination method 2. Matrix algebra 3. Matrix form of systems of equations (LDU decomposition of a matrix, Gauss-Jordan method of determining the inverse matrix) 4. Linear spaces (fundamental subspaces related to matrices, linear independence of vectors, base and dimension of a linear space, rank of a matrix) 5. Orthogonality (projection of a vector on a line and on a subspace, orthogonal complement of space, least squares method, Gram-Schmidt orthogonalization) 6. Matrix determinant (axiomatic definition, Laplace expansion, Cramer's formulas, calculation of the volume of solids) 7. Eigenvalues and eigenvectors (remarks about complex numbers, matrix diagonalization, exponentiation and exponential function of a matrix, spectral decomposition of a symmetric matrix, principal component analysis) 8. Singular value decomposition of matrices (positive definite and positive semidefinite matrices, SVD decomposition) |
Bibliography: |
* Linear Algebra and Its Applications, 4th Edition, R. Strang, Cengage Learning, 2005 |
Learning outcomes: |
Knowledge: - has basic knowledge of combinatorics, graph theory and linear algebra Skills: - uses appropriate software packages to perform calculations on matrices |
Assessment methods and assessment criteria: |
Written exam (50%), 2 colloquiums (25% + 25%), |
Classes in period "Winter semester 2023/24" (past)
Time span: | 2023-10-01 - 2024-01-28 |
Navigate to timetable
MO WYK
CW
CW
CW
TU W TH FR |
Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
Coordinators: | Tomasz Kazana | |
Group instructors: | Tomasz Kazana, Michał Pawłowski, Michał Siemaszko | |
Students list: | (inaccessible to you) | |
Examination: | Examination |
Classes in period "Winter semester 2024/25" (future)
Time span: | 2024-10-01 - 2025-01-26 |
Navigate to timetable
MO TU W TH FR |
Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
Coordinators: | Tomasz Kazana | |
Group instructors: | Tomasz Kazana, Michał Pawłowski, Michał Siemaszko | |
Students list: | (inaccessible to you) | |
Examination: | Examination |
Copyright by University of Warsaw.