Lectures related to Subspaces, Spectra, and Projections

Linear Algebra: Singular Value Decomposition

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

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 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.

Matrix Diagonalization: Spectral Theorem

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

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.

Linear Algebra: Normal Equations and Symmetric Matrices

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

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Orthogonal Bases and Projection

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

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Singular Value Decomposition

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

Spectral Decomposition and SVD

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Orthogonality and Projection

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

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.