Lectures related to Non-Negative Definite Matrices and Covariance Matrices

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

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

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Matrix Diagonalization: Spectral Theorem

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

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

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.

Canonical Correlation Analysis: Overview

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

Principal Component Analysis: Theory and Applications

Covers the theory and applications of Principal Component Analysis, focusing on dimension reduction and eigenvectors.

Characteristic Polynomials and Similar Matrices

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

Principal Component Analysis: Properties and Applications

Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.

Multicollinearity: Dangers and Remedies

Explores the dangers of multicollinearity in linear models and discusses diagnostic methods and remedies.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Diagonalization of Symmetric Matrices

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

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

General Linear Model: Symmetric Matrices

Covers the general linear model and the concept of symmetric matrices.

Multivariate Statistics: Introduction and Methods

Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.

Symmetric Matrices and Eigenvectors

Covers the concept of symmetric matrices, orthogonal bases, and eigenvectors.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.