Objectives of the course: Introduction to linear algebra. Basic algebraic structures groups, fields, linear spaces and properties of algebraic operations. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems:. Cartesian products. Relations orderings, partitions and equivalence relations. Groups, fields, linear spaces.

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Objectives of the course: Introduction to linear algebra. Basic algebraic structures groups, fields, linear spaces and properties of algebraic operations. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems:.

Cartesian products. Relations orderings, partitions and equivalence relations. Groups, fields, linear spaces. Group homomorphism, field isomorphism, vector space linear transformation. Structure of linear spaces. Linear combination of vectors, span of a set of vectors.

Linear independence, basis, and dimension; linear subspace. Coordinates of a vector relative to a basis , matrix representation of a vector,. Linear transformations between finite-dimensional vector spaces. Matrix representations of linear transformations. Algebraic operations on matrices.

Composition of linear transformations and matrix multiplication. Linear combination of vectors and matrix multiplication. Algebraic and geometric structure of the field of complex numbers. Complex numbers as ordered pairs of real numbers, an extension of the real numbers by adjoining an imaginary unit, complex numbers as matrices of linear transformations in R2. Geometric interpretation of complex numbers. Exponentiation and root extraction. Matrices and determinants.

Definitions, properties and calculating. Matrix multiplication non-commutative. Matrix invertibility. Inverce matrix. Oriented volume. Solution methods for systems of linear equations. Kernel and image of a linear transformation, pre-image of a vector and related systems of linear equations. Geometric interpretation of solution sets of homogeneous and non-homogeneous systems of linear equations as linear and affine subspaces in Rn.

Jurlewicz, Z. Skip to main menu Skip to submenu Skip to content. Print syllabus. Choosen plan division: this week course term. Course descriptions are protected by copyright.

You are not logged in log in. Faculty of Mathematics and Natural Sciences. School of Exact Sciences. Level of course: basic Objectives of the course: Introduction to linear algebra. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems: - the linear dependence of a collection of vectors, - properties of linear transformations, - the existence of solutions of systems of linear equations. Prerequisites: no.

Course contents: 1. Relation between two sets, graph, function. Definitions, theorems, proofs. Coordinates of a vector relative to a basis , matrix representation of a vector, 6. Complex numbers as ordered pairs of real numbers, an extension of the real numbers by adjoining an imaginary unit, complex numbers as matrices of linear transformations in R2 9.

Vector and matrix forms of systems of linear equations. Existence and number of solutions: the Kronecker-Capelli theorem.

Assessment methods and assessment criteria:. Choosen plan division: this week course term see course schedule. Classes, 30 hours more information Lectures, 30 hours more information. Daria Michalik. Course - examination Classes - graded credit Lectures - examination.

Introduction to linear algebra. Full description:. Equivalence relations.

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## Some basic information about the module

Definicje, twierdzenia, wzory; [5] Mostowski A. Additional information registration calendar, class conductors, localization and schedules of classes , might be available in the USOSweb system:. Organized by: Faculty of Mathematics and Computer Science. Lecture, discussion, working in groups, heuristic talk, directed reasoning, self-study.

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## Algebra Liniowa 2 - Przykłady I Zadania, Jurlewicz, Skoczylas, Gis 2003

The name of the module: Calculus and linear algebra. The name of the faculty organization unit: The faculty Electrical and Computer Engineering. The name of the module department : Department of Mathematics. The contact details of the coordinator: the building L, room E, phone , kpupka prz. The main aim of study: To acquaint students with the basics of differential and integral calculus of functions of one variable and with the elements of linear algebra. Basic requirements in category knowledge: Basic mathematical knowledge of secondary school.

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## Algebra Liniowa 1 - Kolokwia i Egzaminy - Gewert Skoczylas

Lecture 1 - Preliminaries Presentation of various algebraic objects with particular emphasis on differences and relationships between them. Definitions of number sets: natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, vectors and matrices. Relationships between the objects: the representation of a set of vectors as a matrix, the representation of a complex number as a vector. Lecture 2 - Properties of number sets Divisibility of integers, the congruence modulo, Chinese Remainder Theorem, different number systems. Lecture 3 - Complex numbers Algebra of complex numbers, algebraic and geometric representation. Modulus and argument, trigonometric form, de Moivre's formula.

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