1. SylabUZ
2. Wydział Nauk Ścisłych i Przyrodniczych
3. semestr zimowy 2019/2020
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Algebra liniowa 2

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Algebra liniowa 2 - opis przedmiotu

Cel przedmiotu

The aim of the course is to acquaint the student with the basic of linear algebra.

Wymagania wstępne

Zapisz zmiany

Linear algebra 1

Zakres tematyczny

Lecture

1. Linear spaces: subspaces, spanning sets, linear combination of vectors, linear dependence and independence of vectors, basis and dimension of space, Steinitz theorem. (7 hours)

2. Linear transformations, the kernel and image of a linear transformation, matrices of linear transformations with respect to arbitrary bases. (6 hours)

3. Euclidean space: orthogonality, orthonormal basis. (4 hours)

4. Invariant subspaces, eigenvalues ​​and eigenvectors of linear transformation. (7 hours)

5. Linear and quadratic forms, canonical form of a quadratic form, definiteness and classification of quadratic forms. (6 hours)

Exercise

1. Linear spaces: subspaces, linear dependence and independence of vectors, basis and dimension of space. (6 hours)

2. Linear transformations, the kernel and image of a linear transformation, matrices of linear transformations with respect to arbitrary bases. (6 hours)

3. Euclidean space: orthogonality, Gram-Schmidt orthogonalization, orthonormal basis. (4 hours)

4. Invariant subspaces, eigenvalues ​​and eigenvectors of linear transformations. (6 hours)

5. Linear and quadratic forms, the canonical form of the square form, definiteness and classification of quadratic forms. (4 hours)

Metody kształcenia

Traditional lecturing, solving problems under the supervision of the instructor.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

In order to be allowed to take the exam a student has to have a positive class grade and active participation in classes.

In order to pass the exam a student has to have a positive exam grade.

The final grade is an arithmetic average of the class grade  and the exam grade.

Literatura podstawowa

1. Robert A. Beezer, A First Course in Linear Algebra.

2. Thomas W. Judson, Abstract Algebra:Theory and Applications.

3. Jim Hefferon, Linear Algebra.

Literatura uzupełniająca

1. Serge Lang, Linear Algebra, Undergraduate Texts in Mathematics, 1987.

2. Serge lang, Introduction to Linear Algebra, Undergraduate Texts in Mathematics, 1986.

Uwagi

Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 21-11-2020 06:10)