Lectures related to Orthogonality

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Comparing L1 and L0 + Greedy algorithms

Compares L1 and L0 penalization in linear regression with orthogonal designs using greedy algorithms and empirical comparisons.

Linear Algebra: Organization and Exercises

Covers the organization of linear algebra course and exercises for civil engineering and environmental sciences students.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

Multivariate Methods I

Explores multivariate methods like PCA, SVD, PLS, and ICA for dimensionality reduction in functional brain imaging.

Norm, Dot Product, Orthogonality

Explores norm, dot product, and orthogonality in vector spaces, including properties and inequalities.

Multicollinearity and Model Fit Analysis

Explores the dangers of 'big' models, multicollinearity issues, and model fit analysis in statistics for data science.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Design of Experiments: Response Surface

Explores experimental design methodology, including classic plans, simplex method, and canonical analysis for linear and quadratic models.

Multicollinearity: Dangers and Remedies

Explores the dangers of multicollinearity in linear models and discusses diagnostic methods and remedies.

Orthogonality and Least Squares Method

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

Linear Algebra: Normal Equations and Symmetric Matrices

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Error Analysis for Galerkin Scheme

Covers the error analysis for the Galerkin scheme and the importance of Galerkin orthogonality.

Estimation: Mean-Squared Error and Fisher Information

Explains estimation through mean-squared error and Fisher information in the context of adaptive filters and exponentiated distributions.