Lectures:
Linear relations in description of electrical networks and mechanical systems.
Vektor space, linear mapping, approximation of differential operators.
Matrix of a linear mapping, similarity. Rank and defect, composition, principle of superposition.
Bilineární and quadratic forms. Matrices and classification of bilinear and quadratic forms, application of LDLT decomposition.
Scalar product and orthogonality. Norms, orthogonal systems of vectors, variational principle and the least square method.
skládání lineárních zobrazení, linearita inverzního zobrazení a princip
superpozice. Matice lineárního zobrazení, podobnost.
Projectors. Rotace, reflections, QR decomposition and solution of systems of linear equations. Conjugate gradient method.
Eigenvalues and eigenvectors.. Definition, basic properties, localization of eigenvalues. Spectral decomposition of a symmetric matrix. Matrix calculus fr symmetric matrices, polar decomposition, singular decomposition and gneralized inverse matrix.
Jordan form and matrix functions, applications to ODE.
Generalizations to infinite dimension. Banach space, Hilbert space.
Linear relations in description of electrical networks and mechanical systems.
Vektor space, linear mapping, approximation of differential operators.
Matrix of a linear mapping, similarity. Rank and defect, composition, principle of superposition.
Bilineární and quadratic forms. Matrices and classification of bilinear and quadratic forms, application of LDLT decomposition.
Scalar product and orthogonality. Norms, orthogonal systems of vectors, variational principle and the least square method.
skládání lineárních zobrazení, linearita inverzního zobrazení a princip
superpozice. Matice lineárního zobrazení, podobnost.
Projectors. Rotace, reflections, QR decomposition and solution of systems of linear equations. Conjugate gradient method.
Eigenvalues and eigenvectors.. Definition, basic properties, localization of eigenvalues. Spectral decomposition of a symmetric matrix. Matrix calculus fr symmetric matrices, polar decomposition, singular decomposition and gneralized inverse matrix.
Jordan form and matrix functions, applications to ODE.
Generalizations to infinite dimension. Banach space, Hilbert space.