Applied mathematics


Written exams


Files to download

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.