Lectures related to Direct Methods for Linear Systems

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

Linear Systems: Direct Methods

Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Eigen Library for Linear Algebra

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Matlab: Interactive Mode and Project Steps

Introduces Matlab basics, error handling, and billiards project concepts.

Direct Methods for Solving Linear Equations

Explores direct methods for solving linear equations, LU factorization, Gass elimination, and computational complexity.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Jacobi and Gauss-Seidel methods

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Matrix Multiplication: Applications and Properties

Covers matrix multiplication, properties, and inverses in linear algebra.

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Characteristic Polynomials and Similar Matrices

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

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Linear Algebra: Applications and Matrices

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Numerical Analysis: Linear Systems

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

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.