Lectures related to Jacobi Method

Jacobi Method

Explains the spectral radius of a matrix and its generic definition.

Numerical Analysis: Linear Systems

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Convex Optimization: Notation and Matrix Norms

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Determinant of a Matrix

Covers the properties and calculations of the determinant of a matrix.

Eigenvalues and Similar Matrices

Explores eigenvalues, matrix trace, and similarity, highlighting their significance in matrix properties.

Eigenvalues and Minimal Polynomial

Explores eigenvalues and minimal polynomial, emphasizing their importance in linear algebra.

Diagonalization Techniques: Jacobi Method

Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Matrix Reduction: Part 1

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Density Operator: Quantum Physics II

Covers the concept of matrix to the density operator in quantum physics.

Eigenstate Thermalization Hypothesis

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

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Convergence in Induced Matrix

Covers convergence in induced matrices and advection-diffusion phenomena.

Diagonalizability of Matrices

Explores the diagonalizability of matrices through eigenvectors and eigenvalues, emphasizing their importance and practical implications.