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Linear Algebra 2 - course description

General information
Course name Linear Algebra 2
Course ID 11.1-WK-IiEP-AL2-Ć-S14_pNadGenBT2V3
Faculty Faculty of Exact and Natural Sciences
Field of study computer science and econometrics
Education profile academic
Level of studies First-cycle studies leading to Bachelor's degree
Beginning semester winter term 2019/2020
Course information
Semester 2
ECTS credits to win 5
Course type obligatory
Teaching language polish
Author of syllabus
Classes forms
The class form Hours per semester (full-time) Hours per week (full-time) Hours per semester (part-time) Hours per week (part-time) Form of assignment
Class 30 2 - - Credit with grade
Lecture 30 2 - - Exam

Aim of the course

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

Prerequisites

Linear algebra 1

Scope

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)

Teaching methods

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

Learning outcomes and methods of theirs verification

Outcome description Outcome symbols Methods of verification The class form

Assignment conditions

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.

Recommended reading

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

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

3. Jim Hefferon, Linear Algebra.

Further reading

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

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

Notes


Modified by dr Alina Szelecka (last modification: 21-11-2020 06:10)