714-0404/01 – Linear Algebra (LA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits8
Subject guarantorRNDr. Břetislav Krček, CSc.Subject version guarantorRNDr. Břetislav Krček, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2005/2006
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA37 Mgr. Ilona Hummelová
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3

Subject aims expressed by acquired skills and competences

This course is closed.

Teaching methods

Summary

Polynomials and Algebraic Equations. Linear Spaces. Matrices. Plane and Solid Analytic Geometry.

Compulsory literature:

Sedláček M., Šalounová D., Vrbický J.: Lineární algebra. Ostrava, VŠB 1994. Havel V., Holenda J.: Lineární algebra. Praha, SNTL 1984. Burda P., Havelek R., Hradecká R.: Algebra a analytická geometrie. Ostrava, VŠB-TU 1998. Dostál Z.: Lineární algebra. Ostrava, VŠB-TU 2001.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Algebraické struktury. Polynomy a algebraické rovnice. Racionální lomená funkce. Lineární a vektorové prostory. Lineární kombinace a lineární závislost, báze a dimenze. Souřadnice vektoru. Maticový počet. Operace s maticemi, hodnost matice. Determinant. Inverzní matice, maticové rovnice. Soustavy lineárních rovnic. Frobeniova věta, Gaussova eliminační metoda. Fundamentální systém řešení, obecné řešení soustavy. Cramerovo pravidlo. Vektorové prostory se skalárním součinem. Gramova matice. Ortogonální a ortonornální báze. Gram-Schmidtův ortogonalizační proces. Lineární zobrazení. Definice lineárního zobrazení a jeho vlastnosti, izomorfismus. Lineární závislost funkcí. Spektrální vlastnosti matic. Lineární, bilineární a kvadratické formy. Afinní prostory, vektorová algebra. Analytická geometriie v E3. Kuželosečky a kvadriky. Obecná rovnice kuželosečky, posunutí a otočení. Rovnice kvadrik v kanonickém tvaru, obecná rovnice kvadriky.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner