# Applied mathematics

# 2017/2018

## 2016/2017

## Exercise 5, October 31st, 2016

## Attention! Achtung! Alarm!

Short written test, approximately 30 minutes long.## Exercise 4, October 24th, 2016

- Jordan canonical form. Elementary Jordan blocks.
- Chains of generalized eigenvectors.
- Algorithm for Jordan decomposition.
- Exercises.

## Exercise 3, October 17th, 2016

- Similarity transformation of a matrix. Spectra of similar matrices.
- Operations over diagonal matrices. Taylor expansion of a matrix function, exponential of the matrix.
- Calculation of matrix functions via diagonalization.

## Exercise 2, October 10th, 2016

- Eigenvalues and eigenvectors of matrices. Characteristic polynomial and characteristic (secular) equation. Spectrum and spectral radius of matrix.
- Linear independence of eigenvectors for non-degenerate spectrum. Orthogonality of eigenvectors for Hermitian matrices.
- Inner product and transposition.

## Exercise 1, October 3rd, 2016

- Matrices and basic operations with them: addition, multiplication, transpose, determinant.
- Inverse matrix, Cramer rule, Gauss elimination.
- Kernel of the matrix, linear span, basis of a vector subspace

Last update of this page: June 05 2019 14:54:10.