# 2017/2018

## 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

## List of students

• Jakub Kušnír
• Marius Hegedüs
• Juraj Olejňák