Lectures:
Matrix transformations (Gauss, Jacobi and Hausholder) and decompositions.
Algebraick operations and structures.
Matrix of linear mapping, change of basis, similarity of matrices.
Matrix of bilinear form, change of basis, congruency of syymetric and diagonal matrices.
Variational methods for matrices, least squares and projectors.
Localization of eigenvalues.l
Spectral decomposition of a symmetric matrix.
Scalar function of a symmetric matrix.
Polar decomposition.
Singular decomposition, condition number.
Pseudoinverse matrices.
Jordan form.
Exercises:
Evaluation of LU and QU decomposition.
Examples of algebraic structures..
Evaluation of the matrix of a linear mapping.
Evaluation of matrix of a bilinear form.
Classification of bilinear and quadratic forms.
Numerical solution of the least square problems.
Ecaluation of the spectral decomposition.
Evalution of matrix functions.
Localization of eigenvalues based on cogruency and similarity.
Solution of singular systems and applications of pseudoinverse matrices.
Selected applications of linear algebra (coding, signal analysis, design of search engins, design of efficient numerical algorithms, ...
Projects:
Aplication oriented project in MATLAB (maximum 10 marks).
Matrix transformations (Gauss, Jacobi and Hausholder) and decompositions.
Algebraick operations and structures.
Matrix of linear mapping, change of basis, similarity of matrices.
Matrix of bilinear form, change of basis, congruency of syymetric and diagonal matrices.
Variational methods for matrices, least squares and projectors.
Localization of eigenvalues.l
Spectral decomposition of a symmetric matrix.
Scalar function of a symmetric matrix.
Polar decomposition.
Singular decomposition, condition number.
Pseudoinverse matrices.
Jordan form.
Exercises:
Evaluation of LU and QU decomposition.
Examples of algebraic structures..
Evaluation of the matrix of a linear mapping.
Evaluation of matrix of a bilinear form.
Classification of bilinear and quadratic forms.
Numerical solution of the least square problems.
Ecaluation of the spectral decomposition.
Evalution of matrix functions.
Localization of eigenvalues based on cogruency and similarity.
Solution of singular systems and applications of pseudoinverse matrices.
Selected applications of linear algebra (coding, signal analysis, design of search engins, design of efficient numerical algorithms, ...
Projects:
Aplication oriented project in MATLAB (maximum 10 marks).