Lectures related to Subspaces, Spectra, and Projections

Linear Algebra: Singular Value Decomposition

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

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.

Canonical Correlation Analysis: Overview

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

Linear Algebra Review

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

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Orthogonal Projections and Reflections in 2D

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

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Eigenvalues and Eigenvectors Decomposition Log in to Mediaspace to watch this video

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

Matrix Diagonalization: Spectral Theorem Log in to Mediaspace to watch this video

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

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

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

Spectral Decomposition Log in to Mediaspace to watch this video

Explores spectral and singular value decompositions of matrices.

Decomposition Spectral: Symmetric Matrices Log in to Mediaspace to watch this video

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Matrices and Quadratic Forms: Key Concepts in Linear Algebra Log in to Mediaspace to watch this video

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

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

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

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

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

Orthogonal Bases and Projection Log in to Mediaspace to watch this video

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

Symmetric Matrices: Properties and Decomposition Log in to Mediaspace to watch this video

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

Singular Value Decomposition Log in to Mediaspace to watch this video

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

Linear Algebra: Normal Equations and Symmetric Matrices Log in to Mediaspace to watch this video

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

Spectral Decomposition and SVD Log in to Mediaspace to watch this video

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