Lectures related to Precision Problems: Hilbert Matrix

Singular Value Decomposition: Applications and Interpretation

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

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Characterization of Invertible Matrices

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

Matrix Column Space Analysis

Covers the analysis of the column space of a matrix and its implications.

Matrix Equivalence Theorems

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Linear Algebra: Applications and Matrices

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

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Linear Algebra: Basis and Matrices

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

Characteristic Polynomials and Similar Matrices

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

Matrix of Cofactors and Inverse Matrix Formula

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Matrix Operations: LU Factorization & Linear Independence

Covers LU factorization, linear independence, and matrix equations.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Matrix Operations: Composition and Product

Covers the composition and product of matrices, including matrix multiplication.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

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

Numerical Analysis: Linear Systems

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

Matrix Operations: Transposition, Rank, and Basis Change

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Linear Algebra: Reduction of Linear Application

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