- Description:
-
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.
- Recommended literature:
-
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
- Keywords:
- Determinant, eigenvalues and eigenvectors, diagonalization, quadratic and Hermitian form, diagonalization, inverse operator, normal, Hermitian and unitary operator.
Abbreviations used:
Semester:
- W ... winter semester (usually October - February)
- S ... spring semester (usually March - June)
- W,S ... both semesters
Mode of completion of the course:
- A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
- GA ... Graded Assessment (a grade is awarded for this course)
- EX ... Examination (a grade is awarded for this course)
- A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
- P ... lecture
- C ... seminar
- L ... laboratory
- R ... proseminar
- S ... seminar