Lectures related to Orthogonal Projections: Gram-Schmidt Method

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.

Linear Algebra: Orthogonal Projection and QR Factorization

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

Linear Regression: Least Squares Method

Explains the method of least squares in linear regression to find the best-fitting line to a set of data points.

QR Factorization: Least Squares System Resolution

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

Orthogonal Projections in Linear Algebra

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

Linear Regression Testing

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

Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Subspaces, Spectra, and Projections

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

Least Squares Solutions

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

Orthogonality and Projection

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

Singular Value Decomposition: Applications and Interpretation

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

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

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

Orthogonal Families and Projections

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

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

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

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Regression: High Dimensions

Explores linear regression in high dimensions and practical house price prediction from a dataset.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.