470-2201/02 – Linear Algebra (LA1)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | prof. RNDr. René Kalus, Ph.D. | Subject version guarantor | doc. Mgr. Vít Vondrák, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2010/2011 |
| Intended for the faculties | FEI, USP | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Many engineering problems lead to solution of large-scale systems of linear equations. The aim of this course is to introduce fundamental notions of linear algebra and relate them to applications in electrical engineering. First we shall learn how to solve real and complex systems of linear equations by Gauss elimination method. The systems arises in the analysis of electrical circuits. In an intuitive manner we shall introduce notions such as base of a vector space, linear transformation and using them we will formulate basic linear problems. In the second part of the course, we shall focus on quadratic forms, which are closely related e.g. to electrical potential energy. Further we shall study orthogonality of functions, on which e.g. Fourier analysis of signals rely. Finally, we shall introduce spectral theory with applications to analysis of resonances.
Teaching methods
Lectures
Tutorials
Summary
Linear algebra is a basic tool of formulation and effective solution of technical problems. The students will get knowledge of basic concepts and computational skills of linear algebra.
Compulsory literature:
G. Strang, Video lectures of Linear Algebra on MIT.
R.A. Horn, C.R. Johnson, Matrix Analysis. Cambridge University Press 1990.
Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM 2003.
Recommended literature:
G.H. Golub, C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press 2013.
L.N. Trefethen, D. Bau. Numerical Linear Algebra. SIAM 1997.
J. Liesen, Z. Strakoš, Krylov Subspace Methods: Principles and Analysis. Oxford University Press 2012.
Way of continuous check of knowledge in the course of semester
Verification of study:
Solution of linear systems¨and matrix algebra (max 8b)
Vector spaces, linear mapping, multilinear forms (max 7b)
Homeworks (15b)
Conditions for credit:
Minimum 10 marks of continuous assessment
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Complex numbers
Solution of systems of linear equations by elimation based methods
Algebra of arithmetic vectors and matrices
Inverse matrix
Vector space
Spaces of functions
Derivation and integration of piece-wise linear functions
Linear mapping
Bilinear and quadratic forms
Determinants
Eigenvalues and eigenvectors
An introduction to analytic geometry
Exercises:
Arihmetics of complex numbers
Solution of systems of linear equations
Practicing algebra of arithmetic vectors and matrices
Evaluation of inverse matrix
Examples of vector spaces and deduction from axioms
Evaluation of coordinates of a vector in a given basis
Examples of functional spaces
Examples of linear mappings and evaluation of their matrices
Mtrices of bilinear and quadratic forms
Evaluation of determinants
Evaluation of eigenvalues and eigenvectors
Computational examples from analytic geometry
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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