Lectures:
Linear mappings in elektric networks and mechanical systems.
Vector space, linear mapping and matrices.
Rank, defect, and composition of linear mappings, principle of superposition.
Matrices of linear mappings and similarity.
Bilinear and quadratic forms. Matrices and classification of bilinearr and quadratic forms, congruent matrices and LDLT decomposition.
Scalar product nad orthogonality. Norms, variational principle, the least square method and projectors.
Conjugate gradient method.
Matrix transformations and solution of linear systems.
Eigenvalues and eigenvectors, localization of eigenvalues.
Spectral decomposition of symmetric matrix. Matrix calculus, singular decomposition and pseudoinverse matrices.
Jordan form. Matrix calculus, applications..
Generalizations to infinite dimension. Banach and Hilbert spaces.
Linear mappings in elektric networks and mechanical systems.
Vector space, linear mapping and matrices.
Rank, defect, and composition of linear mappings, principle of superposition.
Matrices of linear mappings and similarity.
Bilinear and quadratic forms. Matrices and classification of bilinearr and quadratic forms, congruent matrices and LDLT decomposition.
Scalar product nad orthogonality. Norms, variational principle, the least square method and projectors.
Conjugate gradient method.
Matrix transformations and solution of linear systems.
Eigenvalues and eigenvectors, localization of eigenvalues.
Spectral decomposition of symmetric matrix. Matrix calculus, singular decomposition and pseudoinverse matrices.
Jordan form. Matrix calculus, applications..
Generalizations to infinite dimension. Banach and Hilbert spaces.