1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Linear Algebra 2

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Linear Algebra 2 - opis przedmiotu

Cel przedmiotu

The aim is for the student to achieve skills and competencies in understanding the basic mathematical topics listed in the thematic scope of the subject and to use the acquired knowledge as linear algebra tools in econometrics and computer science.

Wymagania wstępne

Zapisz zmiany

Linear Algebra 1

Zakres tematyczny

Lecture

1. Linear spaces: subspaces, spanning sets, a 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. (6 hours)
3. Euclidean space: orthogonality, orthonormal basis. (4 hours)
4. Invariant subspaces, eigenvalues, ​​and eigenvectors of linear transformations and matrices. (7 hours)
5. Linear and quadratic forms, canonical form of a quadratic form, definiteness, and classification of quadratic forms. (6 hours)

Class

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. (6 hours)
3. Euclidean space: orthogonality, Gram-Schmidt orthogonalization, orthonormal basis. (4 hours)
4. Invariant subspaces, eigenvalues, ​​and eigenvectors of linear transformations and matrices. (6 hours)
5. Linear and quadratic forms, the canonical form of a square form, definiteness, and classification of quadratic forms. (4 hours)

Metody kształcenia

Traditional lecture; discussion lecture; problem lecture.

Exercises: solving typical tasks illustrating the subject topic, exercises on the application of theory, and solving problem tasks.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The condition for taking the exam is a positive grade from the exercises obtained in two written tests (with tasks of varying grades of difficulty, allowing for checking whether the student has achieved the learning outcomes to a minimum level) and for active participation in the classes.

The condition for passing the course is a positive grade on the exam.

The final grade is the arithmetic mean of the grade from the exercises and the grade from the exam (written or oral).

Literatura podstawowa

1. Robert A. Beezer, A First Course in Linear Algebra.
2. Thomas W. Judson, Abstract Algebra: Theory and Applications.

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 Ewa Synówka (ostatnia modyfikacja: 10-04-2024 19:19)