T. Jurlewicz, Z. Skoczylas – Algebra Liniowa 2 – Definicje, Twierdzenia, – Download as PDF File .pdf), Text File .txt) or read online. Jurlewicz. skoczylas – Algebra Liniowa 2 – Przykłady I Zadania tyczna Wydawnicza GiS, Wrocław [6] T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1. Przykłady i zadania, Oficyna Wydawnicza GiS,. Wrocław [7] M. Gewert. Name in Polish: Elementy algebry liniowej. Main field of study (if Level and form of studies: 1 th level, full time . [2] T. Jurlewicz, Z. Skoczylas, Algebra i geometria analityczna. Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław

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Describe the canonical equations of nondegenerate quadrics in Cartesian coordinates. Give the conditions for the matrix of an operator to be diagonalizable.

Operations on complex numbers. Describe the transformation of the matrix of a linear operator under a change of basis.

## Some basic information about the module

Lecture, 15 hours more information Tutorials, 30 hours more information. Exponential, logarithmic and inverse-trygonometrical functions. Ability to solve equations and inequalities. Determine and compute the oriented measures: Calculus and linear algebra. Rank of a matrix, determinant of a square matrix.

Describe the Gram-Schmidt orthogonalization process. Learning outcomes In terms of knowledge: Composition of a function and inverse function. Derivatives of higher order. Basic requirements in category knowledge: Observe that conic sections are curves obtained by intersecting a cone with a plane. Differential equations and their applications. The name of the faculty organization unit: The positive evaluation of the two colloquia is a prerequisite for admission to the test.

### Katalog przedmiotów

In order to pdzykady tutorial one has to get at least mark 3 from all skills defined in the criteria of passing the module. Lecture, 15 hours more information Tutorials, 15 hours more information.

Matrices and systems of linear equations. Wikipedia english versionhttp: Additional information registration calendar, class conductors, localization and schedules of classesmight be available in the USOSweb system:. Matrix representation of linear transformation. Given the matrix of an operator find eigenvalues and eigenvectors. Departament of Nonlinear Analysis. The preparation for a test: Find the parallel and perpendicular components of a vector relative to another vector.

Definicje, twierdzenia, wzory; [5] Mostowski A.

## Mathematics 1

Describe the types of orthogonal transformations on R3 rotations, reflections and their properties fixed points, eigenvalues and eigenvectors. The final grade algebfa the grade of exam, it can be gone up an extra exam in the case if the grade of classes is higher.

State the polar decomposition theorem for nonsingular operators. Faculty of Mathematics and Computer Science. Explain the geometrical meaning of transformations that shift a conic into canonical form. In terms of social competences: Solving of any systems of linear equations using Cramer theorem and Kronecker-Cappeli theorem.

Szlachtowski, Algebra i geometria afiniczna w zadaniach, Wydawnictwo Naukowo-Techniczne, Warszawa The purpose of this course is to present basic concepts and facts from number theory and algebra of fundamental importance in the further education of information technology – including issues relating to divisibility, modular arithmetic, matrix calculus and analytic geometry. Give example of the canonical Jordan matrix of a linear operator. Convert between polar and Cartesian coordinates.

The student can find information in literature, databases and other data sources; is able to integrate the obtained information, interpret it as well as conclude, formulate and justify opinions.

Explain the relation between the oriented volume and the generalized cross product of a system of n-1 vectors. Rectangular and trygonometric form of a complex number. Write the matrix form of algebraic equations of quadrics in R2 and R3.

The main aim of study: Derive and formulate in terms of the cross product Cramer? Two one-hour exams at class times and a final exam. State the definition of orthogonal trans- formation and describe properties of orthogonal matrices.

Pezykady methods and assessment criteria:. Know that any rotation in R3 is a composition of two reflections. Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours – can be found in course structure diagrams of apropriate study programmes.

Linear algebra Objectives of the course: Describe the canonical equations of quadrics in Rn.