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Lecture
Decomposition LLT: Cholesky
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Matrix Factorizations: LU Decomposition
Introduces LU decomposition for efficient linear equation solving using matrix factorization.
Linear Systems Resolution
Summarizes methods for resolving linear systems, including Gaussian elimination and LU decomposition.
Diagonalization of Symmetric Matrices
Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.
Linear Systems: Choleski Factorisation
Covers the Choleski factorisation method for solving linear systems efficiently.
SVD: Singular Value Decomposition
Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.
Numerical Analysis: Linear Systems
Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.
Matrix Equivalence Theorems
Explores matrix equivalence theorems for systems of equations and least squares solutions.
Spectral Decomposition and SVD
Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.