Lectures related to Multivariate Statistics: Wishart and Hotelling T²

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Principal Components: Properties & Applications

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

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Canonical Correlation Analysis: Overview

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

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Principal Component Analysis: Properties and Applications

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

Multivariate Statistics: Introduction and Methods

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

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Linear Algebra: Singular Value Decomposition

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

Characteristic Polynomials and Similar Matrices

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

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.

Discriminant Analysis: Bayes Rule

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Probability Distributions: Central Limit Theorem and Applications

Discusses probability distributions and the Central Limit Theorem, emphasizing their importance in data science and statistical analysis.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Signal Representations

Covers matrix operations, Fourier transformations, Gaussian models, and signal representations using algebraic methods.