Linear Algebra 2

The course is not on the list Without time-table

Code	Completion	Credits	Range	Language
01LAL2	Z,ZK	4	2P+2C	Czech

Vztahy:

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Outline:

1. Inverse matrix and operator.

2. Permutation and determinant.

3. Spectral theory (eigenvalue, eigenvector, diagonalization).

4. Hermitian and quadratic forms.

5. Scalar product and orthogonality.

6. Metric geometry.

7. Riesz theorem and adjoint operator.

Outline of the exercises:

1. Methods for calculation of inverse matrices.

2. Methods of calculation of determinants.

3. Calculation of eigenvalues and eigenvectors.

4. Hermitian and quadratic forms. Canonical form.

5. Scalar product and orthogonality. Calculation of orthogonal complements.

6. Geometry – exercises and examples.

7. Adjoint operators.

Requirements:

Knowledge of Linear algebra 1 (LAL1) is demanded. Only students who have passed the exam in LAL1 are admitted to the exam in LAL2.

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] L. Dvořáková: Linear algebra 2, textbook, available online on request

[2] T. M. Apostol: Linear Algebra: A First Course with Applications to Differential Equations, John Wiley & Sons, 2014

[3] R. C. Penney: Linear algebra and applications, John Wiley &Sons, 2015

Recommended references:

[3] G. Strang: Introduction to Linear Algebra, Wesley – Cambridge Press, 2016

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: