Lectures related to Stochastic Processes: Generation and Embedding

Stochastic Simulation: Markov Processes Generation

Covers the generation of Markov processes and Poisson processes in stochastic simulation.

Square Matrices: Invertible, Triangular, Diagonal

Explains square matrices, including invertible, triangular, and diagonal matrices, and their properties.

Diagonalization of Matrices

Explores diagonalization of matrices, conditions, invertibility, rank, nullity, and eigenvectors.

Eigenvalue Problems: Methods and Applications

Explores eigenvalue problems, iterative methods, convergence properties, and applications in computational physics.

Triangular Block Matrices

Explores upper triangular block matrices, invertibility, elementary transformations, and determinants with examples.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Jacobi Method: Part I

Introduces the Jacobi method for solving linear systems by iteratively updating the diagonal elements of a matrix.