457-0525/01 – Linear Algebra for IT (LAIT)
Gurantor department | Department of Applied Mathematics | Credits | 6 |
Subject guarantor | doc. Mgr. Vít Vondrák, Ph.D. | Subject version guarantor | doc. Mgr. Vít Vondrák, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | Czech |
Year of introduction | 1999/2000 | Year of cancellation | 2009/2010 |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
To supply working knowledge of basic concepts of linear algebra including their geometric and computational meaning, in order to enable to use these concepts in solution of basic problems of linear algebra. Student should also learn how to use the basic tools of linear algebra in applications.
Teaching methods
Lectures
Tutorials
Project work
Summary
Linear algebra is one of the basic tools of formulation and solution of engineering problems. The students will get in an elementary way basic concepts and comutational skills of linear algebra, including algorithmic aspects that are important in computer implementation.
Compulsory literature:
H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991.
Recommended literature:
S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994
H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989
Way of continuous check of knowledge in the course of semester
Verification of study:
Test on solution of linear systems and matrix algebra (max 8m)
Test on vector spaces, linear mapping and multilinear algebra (max 7m)
Homeworks (15m)
Semestral project
Conditions for credit:
Minimum 15 marks on tests and the homeworks. Submition of solved semestral project.
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
Solution of systems of linear equations by elimination
Algebra aof arithmetic vectors and matrices
Inverse matrices
Vekctor space
Vector spaces of functions
Derivation and definite integral of piecewise linear functions
Linear mapping
Bilinear and quadratic forms
Determinants
Eigenvalues and eigenvectors
An introduction to analytic geometry
Exercises:
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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