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Lecture
Jacobi Method
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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.