Тематический план

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  • Module 1. Background in matrix theory and sparse linear systems

    • Lecture 1. Background in Linear Algebra. Basic definitions. Types and structures of square matrices. Vector and matrix norms.
    • Lecture 2. Range and kernel. Existence of Solution. Orthonormal vectors. Gram-Schmidt process. Thin and full QR-factorization.
    • Lecture 3.  Eigenvalues and their multiplicities. Canonical forms by similarity transformation: diagonal form,  Jordan form, Schur form. Other matrix factorizations: SVD, LU, Cholessky. Positive definite matrices.
    • Lecture 4. Properties of normal and Hermittian matrices. Powers of matrices. Perturbation analysis and condition number. Errors and costs.
    • Lecture 5. Structures and graphs representations of sparse matrices. 
    • Lecture 6. Storage schemes for sparse matrices. Algorithms for matrix by vector multiplication.