714-0404/01 – Linear Algebra (LA)

Gurantor department	Department of Mathematics and Descriptive Geometry	Credits	8
Subject guarantor	RNDr. Břetislav Krček, CSc.	Subject version guarantor	RNDr. Břetislav Krček, CSc.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	winter
		Study language	Czech
Year of introduction	1999/2000	Year of cancellation	2005/2006
Intended for the faculties	FEI	Intended for study types	Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
KRA37	Mgr. Ilona Hummelová

Extent of instruction for forms of study
Form of study	Way 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:

Additional study materials

Study supports in the EduDocs system

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

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 name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (145)	51	3
Examination	Examination	100	0	3
Exercises evaluation	Credit	45	0	3

Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Form	Study language	Tut. centre	Year	Type of duty
2005/2006	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan
2004/2005	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan
2003/2004	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan
2002/2003	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2601T004) Measurement and Control Engineering		P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2612T018) Electronics and Communication Technology		P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(10) Elektrické stroje a přístroje	P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(2642T004) Electrical Machines, Apparatus and Drives	(20) Elektrické pohony a výkonová elektronika	P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(3902T023) Computer Science		P	Czech	Ostrava	1	Compulsory	study plan
2001/2002	(M2612) Electrical Engineering and Computer Science	(3907T001) Electrical Power Engineering		P	Czech	Ostrava	1	Compulsory	study plan
2000/2001	(M2612) Electrical Engineering and Computer Science	(2612T999) Common Base for FEI		P	Czech	Ostrava	1	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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