Lectures related to Krylov subspace

Covers Newton-Krylov-hookstep methods for finding roots of high-dimensional systems.

Explores Newton's method for dynamical systems, GMRES, FGMRES, optimization, multishooting, and trust-region methods.

Covers the Grassmann manifold and retractions on submanifolds.

Covers numerical methods for solving the neutron diffusion equation and addressing heterogeneous effects in thermal reactors.

Explores the heat equation solutions using Fourier series and energy conservation.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Explores the definition and properties of vector subspaces in linear algebra.

Covers strategies for matrix operations and the concept of vector spaces.

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Covers the basics of nuclear reactors, including nuclear fission, neutron diffusion, and multigroup theory.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explores the decomposition principle in linear algebra, showing how a vector space can be split into two subspaces.

Covers the concept of the sum of vector subspaces in an IR-vector space.

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

Explores orthogonal vectors in a vector subspace and their dimension.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Explains how to find free variables in matrix equations and analyze characteristic polynomials.