Оглавление секции
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- Lecture 1. Fundamentals of Linear Algebra. Introduction of elementary notation
- Lecture 2. Types and structures of square matrices. Vector and matrix norms
- Lecture 3. Subspace, range and kernel. Existence of solution. Orthogonality, Gram-Schmidt process and QR-factorization
- Lecture 4. Matrix factorizations (QR, LU, Cholesky)
- Lecture 5. Multiplicities of eigenvalues. Canonical forms of matrices. Diagonal form, jordan form, schur form, singular value decomposition (svd), relation between schur and svd
- Lecture 6. Positive definite matrices. Normal and Hermitian matrices. Powers of matrices. Perturbation analysis. Errors and costs
- Lecture 7. Graph representations of sparse matrices. Permutations and reordering
- Lecture 8. Storage schemes for sparse matrices. Discretization of partial differential equations: overview of methods
- Lecture 9. Discretization of partial differential equations: finite difference method