Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.
Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.
Delves into the proof of the convergence rate theorem for an ergodic Markov chain, emphasizing eigenvalues and detailed balance properties.
Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.
Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.
