Lectures related to Orthogonal Projections in Linear Algebra

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

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

Covers the theorems related to orthogonal projection and orthonormal bases.

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.

Orthogonal Families and Projections

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

Orthogonal Projection in Linear Algebra

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Orthogonal Projection: Uniqueness and Properties

Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Singular Value Decomposition: Applications and Interpretation

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

Orthogonal Projections and Best Approximation

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Orthogonal Projections: Gram-Schmidt Method

Explores orthogonal projections and the Gram-Schmidt method for constructing bases.

Linear Algebra: Orthogonal Projection and QR Factorization

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

QR Factorization: Orthogonal Bases and Matrices

Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.

Orthogonal Projection: Spectral Decomposition

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

Orthogonal Projection: Vector Decomposition

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

Subspaces, Spectra, and Projections

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

Orthogonal Bases in Vector Spaces

Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.

Gram-Schmidt Algorithm

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.