Lectures related to Least Squares Solutions

Least Squares Solutions

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

Matrix Equivalence Theorems

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

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Linear Regression: Basics and Estimation

Covers the basics of linear regression and how to solve estimation problems using least squares and matrix notation.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Singular Value Decomposition: Applications and Interpretation

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

Matrix Factorization: Least Squares Method

Covers the factorization of a matrix and the least squares method.

Linear Regression Testing

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Characterization of Invertible Matrices

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

Singular Value Decomposition: Theory and Applications

Explores Singular Value Decomposition theory, linear system solutions, least squares, and data fitting concepts.

Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Singular Value Decomposition: Applications and Solutions

Explores Singular Value Decomposition, matrix solutions, and least squares regression in data analysis.

Linear Least Squares: Minimizing Error Coefficients

Explores linear least squares, normal equations, and the importance of linear regression in minimizing errors.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Regression: Linear Models

Explores linear regression, least squares, residuals, and confidence intervals in regression models.

Linear Models: Least Squares and QR Factorization

Covers least squares, QR factorization, linear models, and regression analysis with applications to experimental data.

Linear Models: Ridge, OLS and LASSO

Covers linear models like Ridge, OLS, and LASSO, explaining singular values and regression analysis.

Matrix Operations: LU Factorization & Linear Independence

Covers LU factorization, linear independence, and matrix equations.

Linear Regression Basics

Covers the basics of linear regression, including OLS, heteroskedasticity, autocorrelation, instrumental variables, Maximum Likelihood Estimation, time series analysis, and practical advice.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.