Lectures related to Orthogonal Projections and Reflections

Orthogonal Projection: Vector Decomposition

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Vector Spaces: Structure and Bases

Covers vector spaces, bases, and decomposition of vectors in R³.

QR Factorization: Least Squares System Resolution

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

Orthogonality and Projection

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

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Orthogonal Projection: Spectral Decomposition

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Orthogonal Projection: Theory and Applications

Covers the theory of orthogonal projection in vector spaces and its practical applications.

Orthogonal Projections and Reflections in 2D

Covers the geometric description of orthogonal projections and reflections in 2D, focusing on transformations and their properties.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Linear Algebra: Orthogonal Projection and QR Factorization

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Subspaces, Spectra, and Projections

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Orthogonal Projection on Straight Line

Explores orthogonal projection on straight lines in analytic geometry, focusing on projection matrices and symmetrical properties.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Orthogonal Bases and Projection

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Orthogonal Projections: Rectors and Norms

Covers orthogonal projections, rectors, norms, and geometric observations in vector spaces.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.